Tadayuki Watanabe

  1. 1-loop graphs and configuration space integral for embedding spaces.

    Authors: Keiichi Sakai, Tadayuki Watanabe
    Subjects: Geometric Topology
    Abstract

    We will construct differential forms on the embedding spaces using
    configuration space integral associated with 1-loop graphs. In particular, for
    any pair n, j of positive integers with n-j>=2, we show that some linear
    combination of such differential forms together with some correction terms
    coming from a 1-parameter family of immersions gives a closed form on the space
    fEmb(R^j,R^n) of embeddings with 1-parameter families of immersions to the
    trivial. We also show that the closed forms obtained detect nontrivial elements
    of the real homology of the embedding space fEmb(R^j,R^n).

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