2022-08-09T02:03:35Zhttps://kitami-it.repo.nii.ac.jp/oaioai:kitami-it.repo.nii.ac.jp:000081872022-03-15T06:49:42Z1:86Twisted homology and cohomology groups associeted to the Wirtinger integralWatanabe, HumihikoWirtinger integraltheta functiontwisted (co)homology groupde Rham cohomologyThe 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.journal articleMathematical Society of Japan2007application/pdfJournal of the Mathematical Society of Japan45910671080https://kitami-it.repo.nii.ac.jp/record/8187/files/2007_Twisted homology and cohomology groups associeted to the Wirtinger integral.pdfengc2007 Mathematical Society of Japanopen access