|
Higher Lefschetz Traces and Spherical Euler Characteristics
Author(s):
Ross
Geoghegan;
Andrew
Nicas;
John
Oprea
Journal:
Trans. Amer. Math. Soc.
348
(1996),
2039-2062.
MSC (1991):
Primary 55M20;
Secondary 55N45, 55R12, 58F05
MathSciNet review:
1351489
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Higher analogs of the Euler characteristic and Lefschetz number are introduced. It is shown that they possess a variety of properties generalizing known features of those classical invariants. Applications are then given. In particular, it is shown that the higher Euler characteristics are obstructions to homotopy properties such as the TNCZ condition, and to a manifold being homologically Kähler.
References:
- [BG]
- J. C. Becker and D. H. Gottlieb, Transfer maps for fibrations and duality, Compositio Math. 33 (1976), 107--133. MR 55:9087
- [B]
- A. Blanchard, Sur les variétés analytiques complexes, Annales Ec. Norm. Sup. 73 (1956), 157--202. MR 19:316a
- [Bo]
- A. Borel, Seminar on Transformation Groups, Princeton U. Press, Princeton, NJ, 1960. MR 22:7129
- [Br]
- G. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York, 1972. MR 54:1265
- [D1]
- A. Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology 4 (1965), 1--8. MR 33:1850
- [D2]
- A. Dold, The fixed point transfer of fibre-preserving maps, Math. Z. 148 (1976), 215--244. MR 55:6416
- [D3]
- A. Dold, Lectures on algebraic topology, Springer--Verlag, New York, 1980. MR 82c:55001
- [GN]
- R. Geoghegan and A. Nicas, Higher Euler characteristics (I), L'Enseign. Math. 41 (1995), 3--62. CMP 95:15
- [Go1]
- D. Gottlieb, A Certain Subgroup of the Fundamental Group, Amer. J. Math. 87 (1965), 840--856. MR 32:6454
- [Go2]
- D. Gottlieb, Evaluation Subgroups of Homotopy Groups, Amer. J. Math. 91 (1969), 729--756. MR 43:1181
- [Go3]
- D. Gottlieb, Applications of Bundle Map Theory, Trans. Amer. Math. Soc. 171 (1972), 23--50. MR 46:8222
- [Kir]
- F. C. Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry, Math. Notes Vol. 31, Princeton Univ. Press, Princeton, 1984. MR 86i:58050
- [Kn]
- R. J. Knill, On the homology of a fixed point set, Bull. Amer. Math. Soc. 77 (1971), 184--190. MR 45:9320
- [Le]
- J. Leray, Sur les équations et les transformations, J. Math. Pures Appl. (9) 24 (1946), 201--248. MR 7:468g
- [LO]
- G. Lupton and J. Oprea, Cohomologically symplectic spaces: toral actions and the Gottlieb group, Trans. Amer. Math. Soc. 347 (1995), 261--288. MR 95f:57056
- [M]
- S. Mac Lane, Homology, Van Nostrand, Princeton, NJ, 1967. MR 50:2285
- [Mc]
- J. McCleary, User's Guide to Spectral Sequences, Publish or Perish Inc., Wilmington, Del., 1985. MR 87f:55014
- [Sp]
- E. H. Spanier, Algebraic topology, McGraw--Hill, New York, 1966. MR 35:1007
- [W]
- G. W. Whitehead, Elements of Homotopy Theory, Springer-Verlag, New York, 1978. MR 80b:55001
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
55M20,
55N45, 55R12, 58F05
Retrieve articles in all Journals with
MSC (1991):
55M20,
55N45, 55R12, 58F05
Additional Information:
Ross
Geoghegan
Affiliation:
Department of Mathematics, SUNY at Binghamton, Binghamton, New York 13902--6000
Email:
ross@math.binghamton.edu
Andrew
Nicas
Affiliation:
Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Email:
nicas@mcmaster.ca
John
Oprea
Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
Email:
oprea@math.csuohio.edu
DOI:
10.1090/S0002-9947-96-01615-7
PII:
S 0002-9947(96)01615-7
Received by editor(s):
October 27, 1994
Additional Notes:
The first author was partially supported by the National Science Foundation.
The second author was partially supported by the Natural Sciences and Engineering Research Council of Canada.
Copyright of article:
Copyright
1996,
American Mathematical Society
|
