Publications

We list here the publications and preprints of current group members and those of previous members that were made during their stay in the group.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, On the homeomorphism problem of trivalent 2-stratifolds with finite homology groups. Bol. Soc. Mat. Mex. (2024) 30:17.

J. González and J.L. León-Medina, The rational (non-)formality of the non-3-equal manifolds. Preprint arXiv 2401.01449, 2024.

J. Cantarero and A. R. Jiménez, Configuration spaces of commuting elements. To appear in Kyoto J. Math., 2024.

J. Cantarero and J. Gaspar-Lara, Fusion-invariant representations for symmetric groups. To appear in Bull. Iran. Math. Soc., 2024.

G. Longatto Clemente, An overview on real division algebras. Latin American Journal of Mathematics 2, 02 (2023), 43-67.

Y. Félix, M. Fuentes and A. Murillo, Rational homotopy type of relative universal fibrations. Preprint arXiv 2311.14132, 2023.

J. O. Gómez, V. Torres-Castillo and B. Villarreal, On the commutator length of compact Lie groups. Preprint arXiv 2309.02344, 2023.

J. O. Gómez, A family of infinite degree tt-rings. To appear in Bull. London Math. Soc. 2023.

J. Cantarero and Germán Combariza, Uniqueness of factorization for fusion-invariant representations. Comm. Algebra 51 (2023), no. 12, 5187-5208.

J. O. Gómez, On the Picard group of the stable module category for infinite groups. Preprint arXiv 2303.08260, 2023.

B. Villarreal, On the second homotopy group of the classifying space for commutativity in Lie groups. Geom Dedicata 217, 51 (2023).

J. González and J.L. León-Medina, On Lusternik–Schnirelmann category and topological complexity of non-k-equal manifolds. J. Homotopy Relat. Struct. 17, 217–231 (2022).

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, The number of simply-connected trivalent 2-dimensional stratifolds. Topology Appl. 311 (2022), Paper No. 107957, 9 pp.

S. Gritschacher and B. Villarreal, On families of nilpotent subgroups and associated coset posets. J. Homotopy Relat. Str. 63 (2022), no. 4, 493-509.

J. Calles, J. Cantarero, J. O. Gómez and G. Ortega, On the cohomological triviality of the center of the Frattini subgroup. Preprint arXiv 2211.00865, 2022.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, 2-stratifolds with fundamental group Z. Topology Appl. 290 (2021), Paper No. 107590, 14 pp.

J. González, J.L. León-Medina and C. Roque-Márquez, Linear motion planning with controlled collisions and pure planar braids. Homology Homotopy Appl. 23 (2021), no. 1, 275–296.

O. Antolín-Camarena, S. Gritschacher and B. Villarreal, Higher generation by abelian subgroups in Lie groups. Transform. Groups (2021), 1-16.

G. Longatto Clemente and C. H. Silva de Souza, Fractais: figuras de outra dimensão – parte 2. Acta Legalicus 30 (2020).

G. Longatto Clemente and C. H. Silva de Souza, Fractais: figuras de outra dimensão – parte 1. Acta Legalicus 29 (2020).

J. Aguilar-Guzmán, J. González and J.L. León-Medina, Homotopy type of skeleta of the flag complex over a finite vector space and generalized Galois numbers. J. Appl. Comput. Topol. 4 (2020), no. 1, 181–198.

N. Bárcenas and J. Cantarero, A completion theorem for fusion systems. Israel J. Math. 236, 501-531 (2020).

J. Cantarero, N. Castellana and L. Morales, Vector bundles over classifying spaces of p-local finite groups and Benson-Carlson duality. J. Lond. Math. Soc. (2) 101 (2020), no. 1, 1-22.

O. Antolín-Camarena and B. Villarreal, Nilpotent n-tuples in SU(2). Proc. Edinburgh Math. Soc. 63 (2020), no. 4, 1005-1030.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Models of simply-connected trivalent 2-dimensional stratifolds. Bol. Soc. Mat. Mex.(3) 26 (2020), no. 3, 1301-1312.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, 2-stratifold spines of closed 3-manifolds. Osaka J. Math. 57 (2020), no. 2, 267-277.

O. Antolín-Camarena, S. Gritschacher and B. Villarreal, Classifying spaces for commutativity of low-dimensional Lie groups. Math. Proc. Cambridge Philos. Soc. 169 (2020), no. 3, 433-478.

G. Longatto Clemente, Homens de categoria. Acta Legalicus 25 (2019).

G. Longatto Clemente and C. H. Silva de Souza, Uma história dos polígonos regulares. Acta Legalicus 22 (2019).

B. Villarreal and D. Ramras, Commutative cocycles and stable bundles over surfaces. Forum Math. 31 (2019), no. 6, 1395-1415.

O. Antolín-Camarena and B. Villarreal, The complex of affinely commutative sets. Preprint arXiv 1906.07205, 2019.

G. Longatto Clemente and C. H. Silva de Souza, Por que são tão complicadas algumas somas de números naturais?. Acta Legalicus 16 (2018).

A. Adem, J. Cantarero and J. M. Gómez, Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy. J. Math. Phys. 59, 113502 (2018).

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, 2-stratifold groups have solvable word problem. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 112 (2018), no. 3, 803-810.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Classification of simply-connected trivalent 2-dimensional stratifolds. Topology Proc. 52 (2018), 329-340.

B. Villarreal, Cosimplicial groups and spaces of homomorphisms. Algebr. Geom. Topol. 17 (2017), no. 6, 3519-3545.

J. Cantarero and N. Castellana, Unitary embeddings of finite loop spaces. Forum Math. 29 (2017), no. 2, 287-311.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, 2-dimensional stratifolds. A mathematical tribute to Professor José María Montesinos Amilibia 395-405, Dep. Geom. Topol. Fac. Cien. Mat. UCM, Madrid, 2016.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, 2-dimensional stratifolds homotopy equivalent to S^2. Topology Appl. 209 (2016), 56-62.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Categorical group invariants of 3-manifolds. Manuscripta Math. 145 (2014), no. 3-4, 433-448.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Old and new categorical invariants of manifolds. Bol. Soc. Mat. Mex.(3) 20 (2014), no. 2, 177-198.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, On the K-category of 3-manifolds for K a wedge of spheres or projective planes. Topology Proc. 44 (2014), 49-58.

J. Cantarero, J. Scherer and A. Viruel, Nilpotent p-local finite groups. Ark. Mat. 52 (2014), no. 2, 203-225.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Amenable category of three-manifolds. Algebr. Geom. Topol. 13 (2013), no. 2, 905-925.

J. Cantarero, Equivariant K-theory, groupoids and proper actions. J. K-theory 9 (2012), no. 3, 475-501.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Higher dimensional manifolds with S^1-category 2. Math. Z. 271 (2012), no. 1-2, 167-173.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, S^2- and P^2-category of manifolds. Topology Appl. 159 (2012), no. 4, 1052-1058.

J. Cantarero, Twisted K-theory for actions of Lie groupoids and its completion theorem. Math. Z. 268 (2011), no. 1-2, 559-583.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Links in S^3 of S^1-category 2. Topology Proc. 38 (2011), 165-171.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Manifolds with S^1-category 2 have cyclic fundamental groups. Math. Z. 266 (2010), no. 4, 783-788.

J. C. Gómez-Larrañaga, F. González-Acuña and W. H. Heil, Coverings of 3-manifolds by three open solid tori. J. Knot Theory Ramifications 19 (2010), no. 6, 809-820.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Coverings of 3-manifolds by open balls and two open solid tori. Topology Appl. 157 (2010), no. 1, 179-181.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, Fundamental groups of manifolds with S^1-category 2. Math. Z. 259 (2008), no. 2, 419-432.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, A note on Hempel-McMillan coverings of 3-manifolds. Topology Appl. 154 (2007), no. 7, 1363-1367.

J. C. Gómez-Larrañaga, F. González-Acuña and W. Heil, 3-manifolds that are covered by two open bundles. Bol. Soc. Mat. Mexicana (3) 10 (2004), Special Issue, 171-179.

J. C. Gómez-Larrañaga and W. H. Heil, Seifert unions of solid tori. Math. Z. 240 (2002), no. 4, 767-785.

J. C. Gómez-Larrañaga and W. H. Heil, Seifert unions and spaces of graphs in S^3. J. Knot Theory Ramifications 11 (2002), no. 2, 277-282.

J. C. Gómez-Larrañaga and W. Heil, Singhof fillings of closed 3-manifolds. Manuscripta Math. 107 (2002), no. 1, 15-23.

J. C. Gómez-Larrañaga and W. H. Heil, Seifert-Takens-Singhof fillings of 3-manifolds. Proceedings of the Spring Topology and Dynamical Systems Conference (Morelia City, 2001). Topology Proc. 26 (2001/02).

J. C. Gómez-Larrañaga, W. Heil and V. Núñez, Stiefel-Whitney surfaces and the tri-genus of non-orientable 3-manifolds. Manuscripta Math. 100 (1999), no. 4, 405-422.

J. C. Gómez-Larrañaga, F. González-Acuña and V. G. Turaev, Homology category of 3-manifolds. Topology Appl. 95 (1999), no. 3, 217-228.

J. C. Gómez-Larrañaga, W. Heil and V. Núñez, Orientable 3-fillings of non-orientable 3-manifolds. Low-dimensional topology (Knoxville, TN, 1992), 35-40, Conf. Proc. Lecture Notes Geom. Topology, III, Int. Press, Cambridge, MA, 1994.

J. C. Gómez-Larrañaga, W. Heil and V. Núñez, Stiefel-Whitney surfaces and decompositions of 3-manifolds into handlebodies. Topology Appl. 60 (1994), no. 3, 267-280.

J. C. Gómez-Larrañaga and F. González-Acuña, Lusternik-Schnirel'mann category of 3-manifolds. Topology 31 (1992), no. 4, 791-800.

J. C. Gómez-Larrañaga and W. Heil, 3-manifolds that are unions of three handlebodies of genus at most 1. Knots 90 (Osaka, 1990), 477-487, de Gruyter, Berlin (1992).

J. C. Gómez-Larrañaga and F. J. González-Acuña, On the homological category of 3-manifolds. Rev. Mat. Univ. Complut. Madrid 4 (1991), no. 2-3, 213-217.

J. C. Gómez-Larrañaga, F. González-Acuña and J. Hoste, Minimal atlases on 3-manifolds. Math. Proc. Cambridge Philos. Soc. 109 (1991), no. 1, 105-115.

J. C. Gómez-Larrañaga, 3-manifolds which are unions of three solid tori. Manuscripta Math. 59 (1987), no. 3, 325-330.

J. C. Gómez-Larrañaga, Graphs of tangles. Trans. Amer. Math. Soc. 286 (1984), no. 2, 817-830.

J. C. Gómez-Larrañaga, Totally knotted knots are prime. Math. Proc. Cambridge Philos. Soc. 91 (1982), no. 3, 467-472.

Supervised theses

We list here the theses that were supervised by current group members and those by previous members that were supervised during their stay in the group.

Ph.D.

Víctor Antonio Torres Castillo, CIMAT, 2023.
Thesis: Biset functors and the stable homotopy type of classifying spectra of saturated fusion systems.
Supervisors: José Cantarero and Jérôme Scherer.

Juan Omar Gómez Rodríguez, CIMAT, 2023.
Thesis: On the Picard group of the stable module category for infinite groups.
Supervisor: José Cantarero.

Alffer Gustavo Hernández Posada, Universidade Federal de São Carlos, Brazil, 2022.
Thesis: Twisted Borel K-theory and isomorphisms between differential models of K-theory.
Supervisors: José Cantarero and Fabio Ferrari.

Juan Ahtziri González Lemus, CIMAT, 2014.
Thesis: Topological properties of the spaces of simple and convex polygons modulo oriented similarity. (In Spanish)
Supervisor: José Carlos Gómez Larrañaga.

Hugo Cabrera Ibarra, CIMAT, 2001.
Thesis: Classification of rational 3-ovillos. (In Spanish)
Supervisor: José Carlos Gómez Larrañaga.

M.Sc.

Gustavo Navarrete Novelo, Universidad Autónoma de Yucatán, 2022.
Thesis: T-duality in equivariant K-theory (In Spanish).
Supervisors: José Cantarero and J. Matías Navarro

Esteban Heredia Muñoz, CIMAT, 2020.
Thesis: Heegard diagrams with unknotted characteristic curves and trivial fundamental group. (In Spanish)
Supervisor: José Carlos Gómez Larrañaga

Juan Carlos Cruz González, CIMAT, 2019.
Thesis: On the classification of trivalent stratifolds with fundamental group Z/2. (In Spanish)
Supervisor: José Carlos Gómez Larrañaga

Ángel Rolando Jiménez Cruz, Universidad Autónoma de Yucatán, 2019.
Thesis: Invariants of configuration spaces of commuting tuples. (In Spanish)
Supervisors: José Cantarero and J. Matías Navarro

Arfaxard Sánchez Estrella, Universidad Autónoma de Yucatán, 2017.
Thesis: Transfer morphisms for finite transporter categories. (In Spanish)
Supervisors: José Cantarero and Javier A. Díaz

Margarita Angélica Martínez López, CIMAT, 2016.
Thesis: Homological invariants of EI categories.
Supervisors: José Cantarero and Herbert Kanarek

Mario Eudave Muñoz, FC-UNAM, 1986.
Thesis: On prime knots and sum of tangles. (In Spanish)
Supervisor: José Carlos Gómez Larrañaga

B.Sc.

Myriam Hernández Ketchul, Universidad de Guanajuato, 2022.
Thesis: Graph and string representation of trivalent 2-stratifolds with trivial fundamental group.
Supervisor: José Carlos Gómez Larrañaga
Winner of the 2023 Sotero Prieto Award.

Jorge Eduardo Gaspar Lara, Universidad Nacional Autónoma de México, 2020.
Thesis: K-theory and fusion-invariant representations. (In Spanish)
Supervisor: José Cantarero
Winner of the 2021 Sotero Prieto Award.

María Fernanda de la Torre Robles, Universidad de Guanajuato, 2018.
Thesis: Solution to systems of equations of tangles motivated by the molecular biology of DNA. (In Spanish)
Supervisors: José Carlos Gómez Larrañaga and Víctor Manuel Núñez Hernández

Antonio González Fernández, Universidad Autónoma de Yucatán, 2016.
Thesis: Fusion systems for groups, actions and representations. (In Spanish)
Supervisors: José Cantarero and J. Efrén Pérez

Joseph Victor, Stanford University, 2013.
Thesis: Stable homotopy groups of spheres and the Hopf invariant one problem.
Supervisors: José Cantarero and Gunnar Carlsson
Winner of an Undergraduate Research Award 2013 by the mathematics department of Stanford University.

Teresita Ramírez Rosas, Universidad de Guanajuato, 2003.
Thesis: Decomposition of 3-manifolds into prime factors.
Supervisor: José Carlos Gómez Larrañaga

Aldo Hilario Cruz Cota, Universidad de Guanajuato, 2003.
Thesis: Heegard diagrams of genus 2.
Supervisor: José Carlos Gómez Larrañaga

Wilmer Himar Pérez Jiménez, Universidad Juárez Autónoma de Tabasco, 2001.
Thesis: Surfaces generated by a link are equivalent by tubes.
Supervisor: José Carlos Gómez Larrañaga

Christian Edgar Laing Celestino, Universidad de Guanajuato, 2001.
Thesis: The fundamental group of links. (In Spanish)
Supervisor: José Carlos Gómez Larrañaga

Víctor Manuel Núñez Hernández, FC-UNAM, 1986.
Thesis: Seifert fibered spaces. (In Spanish)
Supervisor: José Carlos Gómez Larrañaga