The multiplicativity of fixed point invariants
Abstract
We prove two general factorization theorems for fixed-point invariants of fibrations: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar multiplicativity results for the Lefschetz and Nielsen numbers of a fibration. Moreover, the proofs of these theorems are essentially formal, taking place in the abstract context of bicategorical traces. This makes generalizations to other contexts straightforward.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.0950
- arXiv:
- arXiv:1203.0950
- Bibcode:
- 2012arXiv1203.0950P
- Keywords:
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- Mathematics - Algebraic Topology;
- Mathematics - Category Theory;
- 55M20;
- 18D05;
- 55R05;
- 55P25
- E-Print:
- 24 pages. v3: final version, to appear in AGT