Periodic points and topological restriction homology

Abstract

We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to removing $n$-periodic points from a self-map $f$. Second, this obstruction defines a class in topological restriction homology. We prove these results using duality and trace for bicategories. This allows for immediate generalizations, including a corresponding theorem for the fiberwise Reidemeister trace.

Accepted version. 39 pages, 9 figures

References in corpus (6)

• Duality and traces for indexed monoidal categories
• Cyclotomic structure in the topological Hochschild homology of $DX$
• Topological Hochschild Homology and Higher Characteristics
• Coassembly and the $K$-theory of finite groups
• Comparing cyclotomic structures on different models for topological Hochschild homology
• Homotopical Intersection Theory, II: equivariance

Cited by in corpus (2)

• Unwinding the relative Tate diagonal
• $K$-theory of endomorphisms, the $TR$-trace, and zeta functions