We study the following problem for closed connected oriented manifolds M of dimension 4. Let A be the integral group ring of the fundamental group of M. Suppose that a subset G of H_2(M; A) is a free A-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 the fundamental group of P is isomorphic to the fundamental group of M, the fundamental group of M' is isomorphic to 0, and the tensor product of H_2 (M´ ; Z) with A over Z is isomorphic to G. An answer is given in terms of the fundamental group of M and the intersection forms on H_2 (M ; A) and H_2 (M ; Z).
Connected sums of 4-manifolds / F., Hegenbarth; D., Repovs; Spaggiari, Fulvia. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 146-147:(2005), pp. 209-225. [10.1016/j.topol.2003.02.009]
Connected sums of 4-manifolds
SPAGGIARI, Fulvia
2005
Abstract
We study the following problem for closed connected oriented manifolds M of dimension 4. Let A be the integral group ring of the fundamental group of M. Suppose that a subset G of H_2(M; A) is a free A-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 the fundamental group of P is isomorphic to the fundamental group of M, the fundamental group of M' is isomorphic to 0, and the tensor product of H_2 (M´ ; Z) with A over Z is isomorphic to G. An answer is given in terms of the fundamental group of M and the intersection forms on H_2 (M ; A) and H_2 (M ; Z).
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