Iterated integrals and the loop product
نویسنده
چکیده
The purpose of this paper is to describe string topology from the viewpoint of Chen’s iterated integrals. Let M be a compact closed oriented d-manifold and LM be the free loop space of M , the set of unbased smooth maps from S to M . Let H∗(LM) be the homology of the free loop space shifted by the dimension of the manifold i.e. H∗(LM) = H∗+d(LM). Chas and Sullivan found the product on H∗(LM) which they called loop product [1]:
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