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Higher Lefschetz Traces and
Spherical Euler Characteristics

Authors: Ross Geoghegan, Andrew Nicas and John Oprea
Journal: Trans. Amer. Math. Soc. 348 (1996), 2039-2062
MSC (1991): Primary 55M20; Secondary 55N45, 55R12, 58F05
MathSciNet review: 1351489
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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.

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Additional Information

Ross Geoghegan
Affiliation: Department of Mathematics, SUNY at Binghamton, Binghamton, New York 13902–6000

Andrew Nicas
Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada

John Oprea
Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115

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.
Article copyright: © Copyright 1996 American Mathematical Society

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