Surgery on Simply-Connected Manifolds

Browder, William

doi:10.1007/978-3-642-50020-6

Cited by 330 publications

(255 citation statements)

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“…For the map in the upper left-hand corner, this is the Thom isomorphism [B,II.2.3], and for the other three maps, this is clear.…”

mentioning

confidence: 89%

“…Similarly, we use {D, S} to denote the unique class in H2(N¡, T¡) restricting to the class {D, S} e H2(Di, S¡), with D¡ as above and S¡ = dD¡. This class is simply the Thorn class of the bundle N¡ [B,II.2.3]. The vertical map in the upper lefthand corner is actually the composition of the isomorphism H"~2(E¡, dE¡) = H"~2(N¡, Ni\dEi) with the cup product with the class {D, S} under the cup product map Hn-2(N¡, N¡\dE¡) x H2(N¡, T¡) -» Hn(Ni,dN¡).…”

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confidence: 99%

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On the homology of double branched covers

Lee¹,

Weintraub²

1995

Proc. Amer. Math. Soc.

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Abstract. If it : X -> X is a double branched cover, with branching set F , we relate H.(X : Z2), H,(X : Z2), H.(X, F : Z2), and H»{F : Z2).In this note we present a pair of observations on the homology of double branched covers. These observations arose in our investigations [LW1, LW2], but because of the specialized nature of those investigations and the potential general utility of these observations, we have chosen to present them separately here.All (co)homology in this paper is to be taken with Z2 coefficients. Our first result is a simple generalization of the Gysin sequence, which, however, we have not been able to find in the literature. Theorem 1. Let n : X -> X be a twofold cover of the simplicial complex X, branched over a subcomplex F of X. Let A be an arbitrary subcomplex of X, and set A = n~x(A). If T* denotes the transfer map on homology, then there is a long exact sequence

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“…For the map in the upper left-hand corner, this is the Thom isomorphism [B,II.2.3], and for the other three maps, this is clear.…”

mentioning

confidence: 89%

mentioning

confidence: 99%

On the homology of double branched covers

Lee¹,

Weintraub²

1995

Proc. Amer. Math. Soc.

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“…I do not know what happens in dimension 3. I am grateful to the editor for pointing out that the argument on p. 107 of Browder's book [1], does not carry in the (4k -l)-dimensional case.…”

Section: A Note On Killing Torsion Of Manifolds By Surgery Stavros Pamentioning

confidence: 98%

A Note on Killing Torsion of Manifolds by Surgery

Papastavridis¹

1978

Proceedings of the American Mathematical Society

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“…For 2n < m one can kill elements in the kernel of f M * just as in [11]. This material is thoroughly described in Browder's book "Surgery on Simply Connected Manifolds" ( [4]). This material, when X is not simply connected, is the subject of Wall's book "Surgery on Compact Manifolds" ( [22]), where the general pattern of the above is followed but surgery in the middle dimensions is much more complicated and leads to Wall's Lgroups, in which the obstructions to doing the middle dimension surgery lie.…”

Section: Generalized Groups Of Homotopy Spheresmentioning

confidence: 99%