Reflexive homology and involutive Hochschild homology as equivariant Loday constructions

Abstract

For associative rings with anti-involution several homology theories exists, for instance reflexive homology as studied by Graves and involutive Hochschild homology defined by Fernàndez-València and Giansiracusa. We prove that the corresponding homology groups can be identified with the homotopy groups of an equivariant Loday construction of the one-point compactification of the sign-representation evaluated at the trivial orbit, if we assume that $2$ is invertible and if the underlying abelian group of the ring is flat. We also show a relative version where we consider an associative $k$-algebra with an anti-involution where $k$ is an arbitrary ground ring.

arXiv commentFinal version. To appear in: Proceedings of the Royal Society of Edinburgh Section A: Mathematics

References in corpus (6)

• Crossed simplicial groups and structured surfaces
• Involutive A-infinity algebras and dihedral cohomology
• $K$-theory of Hermitian Mackey functors and a reformulation of the Novikov Conjecture
• Real topological Hochschild homology via the norm and Real Witt vectors
• Reflexive homology
• Loday constructions of Tambara functors