Fixed point theory and the K-theoretic trace

Ross Geoghegan; Andrew Nicas

Banach Center Publications (1999)

  • Volume: 49, Issue: 1, page 137-149
  • ISSN: 0137-6934

Abstract

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The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus K 0 ) and 1-parameter fixed point theory (versus K 1 ). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.

How to cite

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Geoghegan, Ross, and Nicas, Andrew. "Fixed point theory and the K-theoretic trace." Banach Center Publications 49.1 (1999): 137-149. <http://eudml.org/doc/208955>.

@article{Geoghegan1999,
abstract = {The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus $K_0$) and 1-parameter fixed point theory (versus $K_1$). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.},
author = {Geoghegan, Ross, Nicas, Andrew},
journal = {Banach Center Publications},
keywords = {zeta-function; K-theory; classical Nielsen theory; torsion},
language = {eng},
number = {1},
pages = {137-149},
title = {Fixed point theory and the K-theoretic trace},
url = {http://eudml.org/doc/208955},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Geoghegan, Ross
AU - Nicas, Andrew
TI - Fixed point theory and the K-theoretic trace
JO - Banach Center Publications
PY - 1999
VL - 49
IS - 1
SP - 137
EP - 149
AB - The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus $K_0$) and 1-parameter fixed point theory (versus $K_1$). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.
LA - eng
KW - zeta-function; K-theory; classical Nielsen theory; torsion
UR - http://eudml.org/doc/208955
ER -

References

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  19. [R] K. Reidemeister, Automorphismen von Homotopiekettenringen, Math. Ann. 112 (1936), 586-593. 
  20. [RS] C. P. Rourke and B. J. Sanderson, Introduction to Piecewise-Linear Topology, Springer-Verlag, New York, 1972. Zbl0254.57010
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