The Lefschetz number and fixed point index can be thought of as two different descriptions of the same invariant. The Lefschetz number is algebraic and defined using homology. The index is defined more directly from the topology and is a stable homotopy class. Both the Lefschetz number and index admit generalizations to coincidences and the comparison of these invariants retains its central role. In this paper, we show that the identification of the Lefschetz number and index using formal properties of the symmetric monoidal trace extends to coincidence invariants. This perspective on the coincidence index and Lefschetz number also suggests difficulties for generalizations to a coincidence Reidemeister trace.
|Number of pages||19|
|Journal||Journal of Fixed Point Theory and Applications|
|State||Published - Mar 1 2016|
Bibliographical noteFunding Information:
The author was partially supported by NSF grant DMS-1207670.
© 2015, Springer Basel.
- Lefschetz number
- Nielsen number
- Reidemeister trace
- fixed point
ASJC Scopus subject areas
- Modeling and Simulation
- Geometry and Topology
- Applied Mathematics