Adjacent connected sums and torus actions

Author:
Dennis McGavran

Journal:
Trans. Amer. Math. Soc. **251** (1979), 235-254

MSC:
Primary 57S25; Secondary 57N15, 57Q15, 57R05

MathSciNet review:
531977

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Abstract: Let *M* and *N* be closed, compact manifolds of dimension *m* and let *X* be a closed manifold of dimension with embeddings of into *M* and *N*. Suppose the interior of is removed from *M* and *N* and the resulting manifolds are attached via a homeomorphism . Let this homeomorphism be of the form where . The resulting manifold, written as , is called the adjacent connected sum of *M* and *N* along *X*. In this paper definitions and examples are given and the examples are then used to classify actions of the torus on closed, compact, connected, simply connected -manifolds, .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1979-0531977-5

Keywords:
Adjacent connected sums,
torus actions,
simply connected manifolds,
orbit space

Article copyright:
© Copyright 1979
American Mathematical Society