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Homotopy classification of some four-dimensional manifolds. / Ivanov, O. A.

In: Journal of Soviet Mathematics, Vol. 12, No. 1, 01.07.1979, p. 109-114.

Research output: Contribution to journal › Article › peer-review

Harvard

Ivanov, OA 1979, 'Homotopy classification of some four-dimensional manifolds', Journal of Soviet Mathematics, vol. 12, no. 1, pp. 109-114. https://doi.org/10.1007/BF01098420

APA

Ivanov, O. A. (1979). Homotopy classification of some four-dimensional manifolds. Journal of Soviet Mathematics, 12(1), 109-114. https://doi.org/10.1007/BF01098420

Vancouver

Ivanov OA. Homotopy classification of some four-dimensional manifolds. Journal of Soviet Mathematics. 1979 Jul 1;12(1):109-114. https://doi.org/10.1007/BF01098420

Author

Ivanov, O. A. / Homotopy classification of some four-dimensional manifolds. In: Journal of Soviet Mathematics. 1979 ; Vol. 12, No. 1. pp. 109-114.

BibTeX

@article{129c6f6b06fa4abda215da6d0ec74fd1,
title = "Homotopy classification of some four-dimensional manifolds",
abstract = "In this paper there is proved a generalization of the results of Whitehead and Pontryagin on the homotopy classification of closed, simply connected four-manifolds. Let W and M be compact four-dimensional simply connected oriented four-manifolds. By qw is denoted the intersection index on the group H2(W). Basic Result. THEOREM (Extension). Let the groups H1(δW)and H1(δM) be finite and suppose given a homotopy equivalence f:δW→δM. In order that f can be extended to a homotopy equivalence (W,δW)→(M,δM), it is necessary and sufficient that there should exist an isomorphism Ξ, such that the diagram[Figure not available: see fulltext.] is commutative and Ξ*qm=qm.",
author = "Ivanov, {O. A.}",
year = "1979",
month = jul,
day = "1",
doi = "10.1007/BF01098420",
language = "English",
volume = "12",
pages = "109--114",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Homotopy classification of some four-dimensional manifolds

AU - Ivanov, O. A.

PY - 1979/7/1

Y1 - 1979/7/1

N2 - In this paper there is proved a generalization of the results of Whitehead and Pontryagin on the homotopy classification of closed, simply connected four-manifolds. Let W and M be compact four-dimensional simply connected oriented four-manifolds. By qw is denoted the intersection index on the group H2(W). Basic Result. THEOREM (Extension). Let the groups H1(δW)and H1(δM) be finite and suppose given a homotopy equivalence f:δW→δM. In order that f can be extended to a homotopy equivalence (W,δW)→(M,δM), it is necessary and sufficient that there should exist an isomorphism Ξ, such that the diagram[Figure not available: see fulltext.] is commutative and Ξ*qm=qm.

AB - In this paper there is proved a generalization of the results of Whitehead and Pontryagin on the homotopy classification of closed, simply connected four-manifolds. Let W and M be compact four-dimensional simply connected oriented four-manifolds. By qw is denoted the intersection index on the group H2(W). Basic Result. THEOREM (Extension). Let the groups H1(δW)and H1(δM) be finite and suppose given a homotopy equivalence f:δW→δM. In order that f can be extended to a homotopy equivalence (W,δW)→(M,δM), it is necessary and sufficient that there should exist an isomorphism Ξ, such that the diagram[Figure not available: see fulltext.] is commutative and Ξ*qm=qm.

UR - http://www.scopus.com/inward/record.url?scp=34250262422&partnerID=8YFLogxK

U2 - 10.1007/BF01098420

DO - 10.1007/BF01098420

M3 - Article

AN - SCOPUS:34250262422

VL - 12

SP - 109

EP - 114

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 36968209