1-loop graphs and configuration space integral for embedding spaces

• Sakai, Keiichi

• Watanabe, Tadayuki

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.

収録刊行物

• Mathematical Proceedings of the Cambridge Philosophical Society

  Mathematical Proceedings of the Cambridge Philosophical Society 152 (03), 497-533, 2012-05

  Cambridge University Press

キーワード

• General Mathematics

詳細情報

• CRID: 1050564288964146816
• NII論文ID: 120005228644
• NII書誌ID: AA00723568
• DOI: 10.1017/s0305004111000429
• ISSN: 14698064
• ISSN: 03050041
• HANDLE: 2115/52694
• HANDLE: 10091/16236
• Web Site: https://soar-ir.repo.nii.ac.jp/records/11801
• Web Site: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0305004111000429
• 本文言語コード: en
• 資料種別: journal article
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