Coincidence invariants and higher Reidemeister traces

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)147-165
Number of pages19
JournalJournal of Fixed Point Theory and Applications
Issue number1
StatePublished - Mar 1 2016

Bibliographical note

Funding Information:
The author was partially supported by NSF grant DMS-1207670.

Publisher Copyright:
© 2015, Springer Basel.


  • Lefschetz number
  • Nielsen number
  • Reidemeister trace
  • coincidences
  • fixed point

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics


Dive into the research topics of 'Coincidence invariants and higher Reidemeister traces'. Together they form a unique fingerprint.

Cite this