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.

24 pages. v3: final version, to appear in AGT

References in corpus (3)

• Duality and traces for indexed monoidal categories
• Fixed point theory and trace for bicategories
• Shadows and traces in bicategories

Cited by in corpus (8)

• The linearity of traces in monoidal categories and bicategories
• Topological Hochschild Homology and Higher Characteristics
• Traces in symmetric monoidal categories
• Periodic points and topological restriction homology
• Iterated traces in 2-categories and Lefschetz theorems
• Characters and transfer maps via categorified traces
• Coincidence invariants and higher Reidemeister traces
• Euler characteristic and homotopy cardinality