Vector fields on projective Stiefel manifolds and the Browder-Dupont invariant
- Title
- Vector fields on projective Stiefel manifolds and the Browder-Dupont invariant
- Author
- 변양현
- Keywords
- Vector field problem; Projective Stiefel manifold; Span; Browder-Dupont invariant
- Issue Date
- 2020-08
- Publisher
- ELSEVIER
- Citation
- TOPOLOGY AND ITS APPLICATIONS, v. 284, article no. 107364
- Abstract
- We develop strong lower bounds for the span of the projective Stiefel manifolds X-n,X-r = O(n)/(O(n - r) x Z/2), which enable very accurate (in many cases exact) estimates of the span. The technique, for the most part, involves elementary stability properties of vector bundles. However, the case X-n,X-2 with n odd presents extra difficulties, which are partially resolved using the Browder-Dupont invariant. In the process, we observe that the symmetric lift due to Sutherland does not necessarily exist for all odd dimensional closed manifolds, and therefore the Browder-Dupont invariant, as he formulated it, is not defined in general. We will characterize those n's for which the Browder-Dupont invariant is well-defined on X-n,X-2. Then the invariant will be used in this case to obtain the lower bounds for the span as a corollary of a stronger result. (C) 2020 Published by Elsevier B.V.
- URI
- https://www.sciencedirect.com/science/article/pii/S0166864120303072?via%3Dihubhttps://repository.hanyang.ac.kr/handle/20.500.11754/170272
- ISSN
- 0166-8641; 1879-3207
- DOI
- 10.1016/j.topol.2020.107364
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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