1-loop graphs and configuration space integral for embedding spaces

Sakai, Keiichi; Watanabe, Tadayuki

Mathematical Proceedings of the Cambridge Philosophical Society, 2012, 152(03), 497-533

Permalink : https://hdl.handle.net/2115/52694

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MPCPS152-03_497-533	pdf	1.91 MB	987

アクセス権	open access
URI	https://hdl.handle.net/2115/52694
タイトル	1-loop graphs and configuration space integral for embedding spaces
著者	著者名 Sakai, Keiichi
著者	e-Rad_Researcher 70467447 著者名 Watanabe, Tadayuki
言語	英語
発行日	2012-05
出版者	Cambridge University Press
収録物名	Mathematical Proceedings of the Cambridge Philosophical Society
巻(号)	152(03)
ページ	497-533
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
権利情報	Copyright © Cambridge Philosophical Society 2012
PISSN	0305-0041
関連情報	URI http://journals.cambridge.org/action/displayJournal?jid=PSP
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1017/S0305004111000429