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October, 2007 Twisted homology and cohomology groups associated to the Wirtinger integral
Humihiko WATANABE
J. Math. Soc. Japan 59(4): 1067-1080 (October, 2007). DOI: 10.2969/jmsj/05941067

Abstract

The first half of this paper (Section 1) deals with the structure of the twisted homology group associated to the Wirtinger integral. A basis of the first homology group is given, and the vanishing of the homology groups of the other dimensions is proved. The second half (Section 2) deals with the structure of the twisted cohomology groups associated to the Wirtinger integral. The isomorphism between the twisted cohomology groups and the cohomology groups associated to a certain subcomplex of the de Rham complex is established, and a basis of the first cohomology group of this subcomplex (therefore, of the first twisted cohomology group) is given. The vanishing of the cohomology groups of the other dimensions is also proved.

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Humihiko WATANABE. "Twisted homology and cohomology groups associated to the Wirtinger integral." J. Math. Soc. Japan 59 (4) 1067 - 1080, October, 2007. https://doi.org/10.2969/jmsj/05941067

Information

Published: October, 2007
First available in Project Euclid: 10 December 2007

zbMATH: 1188.14014
MathSciNet: MR2370006
Digital Object Identifier: 10.2969/jmsj/05941067

Subjects:
Primary: 33C05
Secondary: 14F40 , 14K25 , 32C35 , 55N25

Keywords: de Rham cohomology , theta function , twisted (co)homology group , Wirtinger integral

Rights: Copyright © 2007 Mathematical Society of Japan

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