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A Note on Doubles of 4-Manifolds

Published online by Cambridge University Press:  20 November 2018

Steven H. Weintraub
Steven H. Weintraub*
Affiliation:
Department of Mathematics Louisiana State University and Agricultural & Mechanical College Baton Rouge, Louisiana 70803
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If M is a simply-connected 4-manifold with boundary, let D(M) denote its double MU∂M(-M). If M is closed, let D(M) denote M#-M. In either case, D(M) is a simply-connected 4-manifold of index zero, and so by a theorem of Wall [8], M#k(S2xS2) must be standard for k sufficiently large, where by standard we mean diffeomorphic to the connected sum of copies of S2 x S2 and S2×S2, the non-trivial S2 bundle over S2 (which is itself diffeomorphic to ℂP2#-ℂP2 [7]). In this paper we give abound on k, in the case where M has no 3-handles.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 367 - 369
Copyright
Copyright © Canadian Mathematical Society 1980

References

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