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Mat. Zametki, 2008, Volume 83, Issue 1, Pages 95–106 (Mi mz3832)  

This article is cited in 1 scientific paper (total in 1 paper)

Two Orientations

E. G. Sklyarenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: All trivializations of an Euclidean line bundle $\pi\colon\mathscr R\to B$ over a connected base $B$ split in two classes which can be naturally named orientations of $\pi$. In the case of an orienting sheaf of a manifold or a vector bundle, they admit a natural interpretation as orientations of these objects. This approach establishes an extension of standard classical constructions to all manifolds and vector bundles independently of orientability restrictions in the usual sense.

Keywords: orientation, orientability, vector bundle, line bundle, structure group, orienting sheaf, twofold covering, cohomology class

DOI: https://doi.org/10.4213/mzm3832

Full text: PDF file (513 kB)
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English version:
Mathematical Notes, 2008, 83:1, 88–96

Bibliographic databases:

UDC: 515.145.25+515.163+515.164.13
Received: 13.03.2007

Citation: E. G. Sklyarenko, “Two Orientations”, Mat. Zametki, 83:1 (2008), 95–106; Math. Notes, 83:1 (2008), 88–96

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. G. Sklyarenko, “The homological degree and Hopf's absolute degree”, Sb. Math., 199:11 (2008), 1687–1713  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математические заметки Mathematical Notes
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