Equivariant method for periodic maps

Author:
Wu Hsiung Huang

Journal:
Trans. Amer. Math. Soc. **189** (1974), 175-183

MSC:
Primary 57D70

DOI:
https://doi.org/10.1090/S0002-9947-1974-0334247-9

MathSciNet review:
0334247

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Abstract: The notion of coherency with submanifolds for a Morse function on a manifold is introduced and discussed in a general way. A Morse inequality for a given periodic transformation which compares the invariants called *q*th Euler numbers on fixed point set and the invariants called *q*th Lefschetz numbers of the transformations is thus obtained. This gives a fixed point theorem in terms of *q*th Lefschetz number for arbitrary *q*.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0334247-9

Keywords:
Periodic transformation,
manifold,
fixed point set,
isometry,
Lefschetz number,
Betti number,
Morse function,
coherency,
fixed point theorem

Article copyright:
© Copyright 1974
American Mathematical Society