Semi-linear homology -spheres and their equivariant inertia groups

Author:
Zhi Lü

Journal:
Trans. Amer. Math. Soc. **356** (2004), 61-71

MSC (2000):
Primary 57S15, 57S17, 57R91, 57R55, 57R67

DOI:
https://doi.org/10.1090/S0002-9947-03-03388-9

Published electronically:
August 25, 2003

MathSciNet review:
2020024

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Abstract: This paper introduces an abelian group for all semi-linear homology -spheres, which corresponds to a known abelian group for all semi-linear homotopy -spheres, where is a compact Lie group and is a -representation with . Then using equivariant surgery techniques, we study the relation between both and when is finite. The main result is that under the conditions that -action is semi-free and with , the homomorphism defined by is an isomorphism if , and a monomorphism if . This is an equivariant analog of a well-known result in differential topology. Such a result is also applied to the equivariant inertia groups of semi-linear homology -spheres.

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Additional Information

**Zhi Lü**

Affiliation:
Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

Address at time of publication:
Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Email:
zlu@fudan.edu.cn

DOI:
https://doi.org/10.1090/S0002-9947-03-03388-9

Keywords:
Semi-linear homology $G$-sphere,
equivariant inertia group,
$G$-action,
representation,
surgery

Received by editor(s):
July 3, 2000

Published electronically:
August 25, 2003

Additional Notes:
This work was supported by the Japanese Government Scholarship, and partially supported by the research fund of the Ministry of Education in China and the JSPS Postdoctoral Fellowship (No. P02299).

Article copyright:
© Copyright 2003
American Mathematical Society