Cycle-free chessboard complexes and symmetric homology of algebras

TL;DR

This paper investigates the connectivity of cycle-free chessboard complexes, confirming a conjecture and advancing understanding of their role in symmetric homology of algebras.

Contribution

It proves a key conjecture about the connectivity of cycle-free chessboard complexes, enhancing their application in algebraic topology.

Findings

Confirmed a strengthened conjecture on connectivity

Established new properties of cycle-free chessboard complexes

Improved understanding of symmetric homology computations

Abstract

Chessboard complexes and their relatives have been one of important recurring themes of topological combinatorics. Closely related ``cycle-free chessboard complexes'' have been recently introduced by Ault and Fiedorowicz as a tool for computing symmetric analogues of the cyclic homology of algebras. We study connectivity properties of these complexes and prove a result that confirms a strengthened conjecture of Ault and Fiedorowicz.