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1-loop graphs and configuration space integral for embedding spaces
| Title: | 1-loop graphs and configuration space integral for embedding spaces |
| Authors: | Sakai, Keiichi Browse this author | | Watanabe, Tadayuki Browse this author →KAKEN DB |
| Issue Date: | May-2012 |
| Publisher: | Cambridge University Press |
| Journal Title: | Mathematical Proceedings of the Cambridge Philosophical Society |
| Volume: | 152 |
| Issue: | 03 |
| Start Page: | 497 |
| End Page: | 533 |
| Publisher DOI: | 10.1017/S0305004111000429 |
| Abstract: | We will construct differential forms on the embedding spaces Emb(ℝj, ℝn) 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(ℝj, ℝn) by Emb[￣] (ℝj, ℝn), the homotopy fiber of the inclusion Emb(ℝj, ℝn) ↪ Imm(ℝj, ℝn). We also show that the closed forms obtained give rise to nontrivial cohomology classes, evaluating them on some cycles of Emb(ℝj, ℝn) and Emb[￣] (ℝj, ℝn). In particular we obtain nontrivial cohomology classes (for example, in H3(Emb(ℝ2, ℝ5))) of higher degrees than those of the first nonvanishing homotopy groups. |
| Rights: | Copyright © Cambridge Philosophical Society 2012 |
| Relation: | http://journals.cambridge.org/action/displayJournal?jid=PSP |
| Type: | article |
| URI: | http://hdl.handle.net/2115/52694 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 渡邉 忠之
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