The linearity of fixed point invariants

Kate Ponto, Michael Shulman

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


We prove two general decomposition theorems for fixed-point invariants: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar additivity results for these invariants. Moreover, the proofs of these theorems are essentially formal, taking place in the abstract context of bicategorical traces. This makes it straightforward to generalize the theory to analogous invariants in other contexts, such as equivariant and fiberwise homotopy theory.

Original languageEnglish
Title of host publicationContemporary Mathematics
Number of pages32
StatePublished - 2018

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Bibliographical note

Funding Information:
2010 Mathematics Subject Classification. 18D05, 18D10, 55M20. Key words and phrases. trace, additivity, derivators, monoidal model category. The first author was partially supported by NSF grant DMS-1207670. The second author was partially supported by an NSF postdoctoral fellowship and NSF grant DMS-1128155, and appreciates the hospitality of the University of Kentucky. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Publisher Copyright:
© 2018 Kate Ponto and Michael Shulman.


  • Additivity
  • Derivators
  • Monoidal model category
  • Trace

ASJC Scopus subject areas

  • Mathematics (all)


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