We study the following problem for closed connected oriented manifolds M of dimension 4. Let be the integral group ring of the fundamental group π1(M). Suppose GH2(M;Λ) is a free Λ-submodule. When do there exist closed connected 4-manifolds P and M′ such that M is homotopy equivalent to the connected sum P # M′, where π1(P)π1(M), π1(M′)0, and . An answer is given in terms of π1(M) and the intersection forms on H2(M;Λ) and .
Connected sums of 4-manifolds / Friedrich Hegenbarth, Dusan Repovs, Fulvia Spaggiari.. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - 146/147(2005), pp. 209-225.
Connected sums of 4-manifolds
Friedrich Hegenbarth;
2005
Abstract
We study the following problem for closed connected oriented manifolds M of dimension 4. Let be the integral group ring of the fundamental group π1(M). Suppose GH2(M;Λ) is a free Λ-submodule. When do there exist closed connected 4-manifolds P and M′ such that M is homotopy equivalent to the connected sum P # M′, where π1(P)π1(M), π1(M′)0, and . An answer is given in terms of π1(M) and the intersection forms on H2(M;Λ) and .
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