40 citations · 61 across the 12 of their papers we have counts for
13 papers
Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence
Daniel Sheinbaum, Omar Antolín-Camarena
Freed and Hopkins developed an ansatz for classifying interacting SPT phases using invertible field theories with a natural Free to Interacting (FTI) map from free fermion phases.…
Centralizers and classifying spaces for commutativity of
Omar Antol\'ın-Camarena, Ramón Flores, Luis Jorge Sánchez Saldaña
We compute the homotopy type of the classifying space for commutativity introduced by Adem, F. Cohen and Torres-Giese for the group $\SL_2(\Z[1/p])$, both as a discrete topological…
The nine model category structures on the category of sets
Omar Antolín-Camarena, Tobias Barthel
We give a proof of the folklore theorem, attributed to Goodwillie, that there are precisely nine model structures on the category of sets. This result is deduced fro…
Poincaré-Birkhoff-Witt Theorems in Higher Algebra
Omar Antolín-Camarena, Lukas Brantner, Gijs Heuts
We extend the classical Poincaré-Birkhoff-Witt theorem to higher algebra by establishing a version that applies to spectral Lie algebras. We deduce this statement from a basic rela…
Topological components of spaces of commuting elements in connected nilpotent Lie groups
Omar Antolín-Camarena, Bernardo Villarreal
We study the homotopy type of spaces of commuting elements in connected nilpotent Lie groups, via almost commuting elements in their Lie algebras. We give a necessary and sufficien…
The classifying space for commutativity of geometric orientable 3-manifold groups
Omar Antolín-Camarena, Luis Eduardo García-Hernández, Luis Jorge Sánchez Saldaña
For a topological group let be the total space of the universal transitionally commutative principal -bundle as defined by Adem--Cohen--Torres-Giese. S…
Higher generation by abelian subgroups in Lie groups
Omar Antolín-Camarena, Simon Gritschacher, Bernardo Villarreal
To a compact Lie group one can associate a space akin to the poset of cosets of abelian subgroups of a discrete group. The space was introduced by Adem, F. Co…
The Complex of Affinely Commutative Sets
Omar Antolín-Camarena, Bernardo Villarreal
We show that for some classes of groups , the homotopy fiber of the inclusion of the classifying space for commutativity into the class…
Classifying spaces for commutativity of low-dimensional Lie groups
Omar Antolín-Camarena, Simon Gritschacher, Bernardo Villarreal
For each of the groups , we compute the integral and -cohomology rings of (the classifying space for commutativity of ), th…
Nilpotent -tuples in
Omar Antolín Camarena, Bernardo Villarreal
We describe the connected components of the space of homomorphisms for a discrete nilpotent group . The connected components arising from homomorphisms wit…
A simple universal property of Thom ring spectra
Omar Antolín-Camarena, Tobias Barthel
We give a simple universal property of the multiplicative structure on the Thom spectrum of an -fold loop map, obtained as a special case of a characterization of the algebra st…
Chromatic fracture cubes
Omar Antolín-Camarena, Tobias Barthel
In this note, we construct a general form of the chromatic fracture cube, using a convenient characterization of the total homotopy fiber, and deduce a decomposition of the E(n)-lo…
Computing arithmetic invariants for hyperbolic reflection groups
Omar Antolin-Camarena, Gregory R. Maloney, Roland K. W. Roeder
We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in , the commensurability inva…