Some results on orientation preserving involutions

Author:
David E. Gibbs

Journal:
Trans. Amer. Math. Soc. **218** (1976), 321-332

MSC:
Primary 57D85

MathSciNet review:
0410770

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Abstract: The bordism of orientation preserving differentiable involutions is studied by use of the signature-like invariant . The equivariant Witt ring is calculated and is shown to be isomorphic under ab to the effective part of . Modulo 2 relations are established between the representation of the involution on and and , where is the Euler characteristic of those components of the fixed point set with dimensions congruent to *i* modulo 4. For manifolds of dimension , it is shown that . Finally the ideal consisting of those elements of admitting a representative of type II is determined.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0410770-5

Keywords:
Equivariant bordism,
Euler characteristic,
orientation preserving involution,
representation,
Witt ring

Article copyright:
© Copyright 1976
American Mathematical Society