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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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