Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 51, Number 2 (1999), 413-435.
On the nonuniqueness of equivariant connected sums
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.
J. Math. Soc. Japan, Volume 51, Number 2 (1999), 413-435.
First available in Project Euclid: 10 June 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57S15: Compact Lie groups of differentiable transformations 57S17: Finite transformation groups
Secondary: 57R55: Differentiable structures 57R67: Surgery obstructions, Wall groups [See also 19J25]
Connected sum equivariant almost diffeomorphism equivariant inertia group tangential representations at fixed points Gap Hypothesis generalized Atiyah-Singer invariants semifree circle actions
MASUDA, Mikiya; SCHULTZ, Reinhard. On the nonuniqueness of equivariant connected sums. J. Math. Soc. Japan 51 (1999), no. 2, 413--435. doi:10.2969/jmsj/05120413. https://projecteuclid.org/euclid.jmsj/1213108025