2024-03-28T09:31:53Z
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oai:soar-ir.repo.nii.ac.jp:00011801
2022-12-14T04:12:48Z
1169:1170
1-loop graphs and configuration space integral for embedding spaces
Sakai, Keiichi
Watanabe, Tadayuki
Copyright© 2012 Cambridge Philosophical Society
We 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.
Article
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. 152:497-533 (2012)
CAMBRIDGE UNIV PRESS
2012-05
eng
journal article
VoR
http://hdl.handle.net/10091/16236
https://soar-ir.repo.nii.ac.jp/records/11801
https://doi.org/10.1017/S0305004111000429
10.1017/S0305004111000429
0305-0041
AA00723568
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
152
497
533
https://soar-ir.repo.nii.ac.jp/record/11801/files/1loop_graphs_configuration_space_integral.pdf
application/pdf
2.4 MB
2015-09-28