Pirashvili–Richter-type theorems for the reflexive and dihedral homology theories
Year: 2025
Type: article
Abstract: Reflexive homology and dihedral homology are the homology theories associated to the reflexive and dihedral crossed simplicial groups respectively. The former has recently been shown to capture interesting information about C 2 -equivariant homotopy theory and its structure is related to the study of “real” objects in algebraic topology. The latter has long been of interest for its applications in O ( 2 ) -equivariant homotopy theory and connections to Hermitian algebraic K -theory. In this paper, we show that the reflexive and dihedral homology theories can be interpreted as functor homology over categories of non-commutative sets, after the fashion of Pirashvili and Richter’s result for the Hochschild and cyclic homology theories.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.698
Author: Daniel Graves
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408199220