On the nonuniqueness of equivariant connected sums
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- MASUDA Mikiya
- Department of Mathematics Osaka City University
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- SCHULTZ Reinhard
- Department of Mathematics University of California
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Abstract
In both ordinary and equivariant 3-dimensional topology there are strong uniqueness theorems for connected sum decompositions of manifolds, but in ordinary higher dimensional topology such decompositions need not be unique. This paper constructs families of manifolds with smooth group actions that are equivariantly almost diffeomorphic but have infinitely many inequivalent equivariant connected sum repre-sentations for which one summand is fixed. The examples imply the need for restrictions in any attempt to define Atiyah-Singer type invariants for odd dimensional manifolds with nonfree smooth group actions. Applications to other questions are also considered.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 51 (2), 413-435, 1999
The Mathematical Society of Japan
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Details
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- CRID
- 1390282680092759296
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- NII Article ID
- 10002151712
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- MRID
- 1674757
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- NDL BIB ID
- 4712219
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed