2021-10-19T11:56:41Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000118012021-09-02T06:12:07Z1169:11701-loop graphs and configuration space integral for embedding spacesSakai, KeiichiWatanabe, TadayukiWe will construct differential forms on the embedding spaces Emb(R-j, R-n) for n-j >= 2 using configuration space integral associated with 1-loop graphs, and show that some linear combinations of these forms are closed in some dimensions. There are other dimensions in which we can show the closedness if we replace Emb(R-j, R-n) by (Emb) over bar (R-j, R-n), the homotopy fiber of the inclusion Emb(R-j, R-n) hooked right arrow Imm(R-j, R-n). We also show that the closed forms obtained give rise to nontrivial cohomology classes, evaluating them on some cycles of Emb(R-j, R-n) and (Emb) over bar (R-j, R-n). In particular we obtain nontrivial cohomology classes (for example, in H-3(Emb(R-2, R-5))) of higher degrees than those of the first nonvanishing homotopy groups.ArticleMATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. 152:497-533 (2012)journal articleCAMBRIDGE UNIV PRESS2012-05application/pdfMATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY1524975330305-0041AA00723568https://soar-ir.repo.nii.ac.jp/record/11801/files/1loop_graphs_configuration_space_integral.pdfeng10.1017/S0305004111000429https://doi.org/10.1017/S0305004111000429CopyrightÂ© 2012 Cambridge Philosophical Society