h–cobordisms between 1–connected 4–manifolds
Geometry & topology, Tome 5 (2001) no. 1, pp. 1-6.

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In this note we classify the diffeomorphism classes rel. boundary of smooth h–cobordisms between two fixed 1–connected 4–manifolds in terms of isometries between the intersection forms.

DOI : 10.2140/gt.2001.5.1
Keywords: 4–manifolds, smooth $h$–cobordisms, surgery

Kreck, Matthias 1

1 Mathematisches Institut, Universität Heidelberg, 69120 Heidelberg, Germany, Mathematisches Forschungsinstitut Oberwolfach, 77709 Oberwolfach, Germany
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Kreck, Matthias. h–cobordisms between 1–connected 4–manifolds. Geometry & topology, Tome 5 (2001) no. 1, pp. 1-6. doi : 10.2140/gt.2001.5.1. http://geodesic.mathdoc.fr/articles/10.2140/gt.2001.5.1/

[1] T D Cochran, N Habegger, On the homotopy theory of simply connected four manifolds, Topology 29 (1990) 419

[2] S K Donaldson, Irrationality and the $h$–cobordism conjecture, J. Differential Geom. 26 (1987) 141

[3] M H Freedman, F Quinn, Topology of 4–manifolds, Princeton Mathematical Series 39, Princeton University Press (1990)

[4] I Hambleton, M Kreck, Cancellation, elliptic surfaces and the topology of certain four-manifolds, J. Reine Angew. Math. 444 (1993) 79

[5] M Kreck, Isotopy classes of diffeomorphisms of $(k-1)$–connected almost-parallelizable $2k$–manifolds, from: "Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978)", Lecture Notes in Math. 763, Springer (1979) 643

[6] M Kreck, Surgery and duality, Ann. of Math. $(2)$ 149 (1999) 707

[7] J Milnor, On simply connected 4–manifolds, from: "Symposium internacional de topología algebraica International symposi um on algebraic topology", Universidad Nacional Autónoma de México and UNESCO, Mexico City (1958) 122

[8] J W Morgan, Z Szabó, Complexity of 4–dimensional $h$–cobordisms, Invent. Math. 136 (1999) 273

[9] B Perron, Pseudo-isotopies et isotopies en dimension quatre dans la catégorie topologique, Topology 25 (1986) 381

[10] F Quinn, Isotopy of 4–manifolds, J. Differential Geom. 24 (1986) 343

[11] C T C Wall, Surgery on compact manifolds, London Mathematical Society Monographs 1, Academic Press (1970)

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