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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.12871
- arXiv:
- arXiv:1811.12871
- Bibcode:
- 2018arXiv181112871M
- Keywords:
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- Mathematics - Algebraic Topology;
- Mathematics - K-Theory and Homology;
- 55M20;
- 55P42;
- 18D05;
- 55R70;
- 18D30;
- 55P91
- E-Print:
- Accepted version. 39 pages, 9 figures