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1999 | 49 | 1 | 137-149
Tytuł artykułu

Fixed point theory and the K-theoretic trace

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
49
Numer
1
Strony
137-149
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000 USA
autor
  • Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Bibliografia
  • [Ba] H. Bass, Euler characteristics and characters of discrete groups, Invent. Math. 35 (1976), 155-196.
  • [B] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott Foresman, Chicago, 1971.
  • [Br] K. S. Brown, Cohomology of Groups, Springer-Verlag, New York, 1982.
  • [BG] K. S. Brown and R. Geoghegan, An infinite dimensional torsion-free $FP_∞$ group, Invent. Math. 77 (1984), 367-381.
  • [C] M. M. Cohen, A Course in Simple-Homotopy Theory, Springer-Verlag, New York, 1973.
  • [DG] D. Dimovski and R. Geoghegan, One-parameter fixed point theory, Forum Math. 2 (1990), 125-154.
  • [F] D. Fried, Homological identities for closed orbits, Invent. Math. 71 (1983), 419-442.
  • [G1] R. Geoghegan, Fixed points in finitely dominated compacta: the geometric meaning of a conjecture of H. Bass, in: Shape Theory and Geometric Topology, Lecture Notes in Math. 870, Springer-Verlag, New York, 1981, 6-22.
  • [G2] R. Geoghegan, Nielsen fixed point theory, in: Handbook of Geometric Topology, (to be published by Elsevier).
  • [GN1] R. Geoghegan and A. Nicas, Parametrized Lefschetz-Nielsen fixed point theory and Hochschild homology traces, Amer. J. Math. 116 (1994), 397-446.
  • [GN2] R. Geoghegan and A. Nicas, Trace and torsion in the theory of flows, Topology 33 (1994), 683-719.
  • [GN3] R. Geoghegan and A. Nicas, Higher Euler characteristics (I), Enseign. Math. 41 (1995), 3-62.
  • [GN4] R. Geoghegan and A. Nicas, A Hochschild homology Euler characteristic for circle actions, K-theory (to appear).
  • [GNO] R. Geoghegan, A. Nicas and J. Oprea, Higher Lefschetz traces and spherical Euler characteristics, Trans. Amer. Math. Soc. 348 (1996), 2039-2062.
  • [HH] H. M. Hastings and A. Heller, Homotopy idempotents on finite dimensional complexes split, Proc. Amer. Math. Soc. 85 (1982), 619-622.
  • [J] B. J. Jiang, Estimation of the number of periodic orbits, Pacific J. Math. 172 (1996), 151-185.
  • [K] M. A. Kervaire, Le théorème de Barden-Mazur-Stallings, Comment. Math. Helv. 40 (1965), 31-42.
  • [M] J. Milnor, Infinite cyclic coverings, in: Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967), Prindle, Weber & Schmidt, Boston, 1968, 115-133.
  • [R] K. Reidemeister, Automorphismen von Homotopiekettenringen, Math. Ann. 112 (1936), 586-593.
  • [RS] C. P. Rourke and B. J. Sanderson, Introduction to Piecewise-Linear Topology, Springer-Verlag, New York, 1972.
  • [St] J. Stallings, Centerless groups - An algebraic formulation of Gottlieb's theorem, Topology 4 (1965), 129-134.
  • [Wa] C. T. C. Wall, Finiteness conditions for CW complexes, Ann. of Math. 81 (1965), 56-69.
  • [W] F. Wecken, Fixpunktklassen, I, II, III, Math. Ann. 117 (1941), 659-671, 118 (1942), 216-234, 118 (1942), 544-577.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv49i1p137bwm
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