772 research outputs found
1-loop graphs and configuration space integral for embedding spaces
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 fEmb(R^j,R^n), the homotopy fiber of the inclusion
Emb(R^j,R^n) -> 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 fEmb(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.Comment: 35 pages, to appear in Mathematical Proceedings of the Cambridge
Philosophical Societ
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