11 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…