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April, 1999 On the nonuniqueness of equivariant connected sums
Mikiya MASUDA, Reinhard SCHULTZ
J. Math. Soc. Japan 51(2): 413-435 (April, 1999). DOI: 10.2969/jmsj/05120413


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 representations 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.


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Mikiya MASUDA. Reinhard SCHULTZ. "On the nonuniqueness of equivariant connected sums." J. Math. Soc. Japan 51 (2) 413 - 435, April, 1999.


Published: April, 1999
First available in Project Euclid: 10 June 2008

zbMATH: 0928.57036
MathSciNet: MR1674757
Digital Object Identifier: 10.2969/jmsj/05120413

Primary: 57S15 , 57S17
Secondary: 57R55 , 57R67

Keywords: connected sum , equivariant almost diffeomorphism , equivariant inertia group , Gap Hypothesis , generalized Atiyah-Singer invariants , semifree circle actions , tangential representations at fixed points

Rights: Copyright © 1999 Mathematical Society of Japan


Vol.51 • No. 2 • April, 1999
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