Universität zu Köln

Konstantis, Panagiotis (2021). VECTOR BUNDLES AND COHOMOTOPIES OF SPIN 5-MANIFOLDS. Homol. Homotopy Appl., 23 (1). S. 143 - 159. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1532-0081

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Abstract

The purpose of this paper is two-fold: On the one side we would like to fill a gap on the classification of vector bundles over 5-manifolds. Therefore it will be necessary to study quaternionic line bundles over 5-manifolds which are in 1-1 correspondence to elements in the cohomotopy group pi(4)(M) = [M, S-4] of M. From results in [22, 24] this group fits into a short exact sequence, which splits into H-4(M; Z)circle plus Z(2) if M is spin. The second intent is to provide a bordism theoretic splitting map for this short exact sequence, which will lead to a Z(2)-invariant for quaternionic line bundles. This invariant is related to the generalized Kervaire semi-characteristic of [23].

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Konstantis, Panagiotis UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-565230
DOI:	10.4310/HHA.2021.v23.n1.a9
Journal or Publication Title:	Homol. Homotopy Appl.
Volume:	23
Number:	1
Page Range:	S. 143 - 159
Date:	2021
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1532-0081
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CLASSIFICATION; FIELDS Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/56523