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On Simply‐Connected 4‐Manifolds
Author(s) -
Wall C. T. C.
Publication year - 1964
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s1-39.1.141
Subject(s) - citation , computer science , information retrieval , combinatorics , library science , mathematics
This paper concerns (but does not succeed in performing) the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds. It arises out of the observation (due to Pontrjagin and Milnor [2]) that if two such manifolds Mx and M2 have isomorphic quadratic forms of intersection numbers on #2(Jft-), then there is a map / : M1-^-Mi which is a homotopy equivalence and induces the tangent bundle of Mx from that of M2 (see below). The same result is also known to follow from /i-cobordism of Mx to M2 [4]. This suggests