On the nonuniqueness of equivariant connected sums

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概要

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• 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.

• 社団法人 日本数学会の論文

著者

• Schultz Reinhard

  Department Of Mathematics University Of California

• Masuda Mikiya

  Department Of Mathematics Osaka City University

関連論文

• An invariant of manifold pairs and its applications
• Unitary toric manifolds, multi-fans and equivariant index
• On the nonuniqueness of equivariant connected sums

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