I will describe how rational homology of a space closely related to the space of embeddings of a manifold in a Euclidean space can be studied using orthogonal calculus of functors. In particular, under appropriate dimensional assumptions, the orthogonal calculus tower for this space splits into the product of its layers. Equivalently, the rational homology spectral sequence associated to this tower collapses at E^1. One consquence is that the rational homology groups of this space of embeddings are determined by the rational homotopy type of the manifold. The main tools in the proofs are embedding calculus of functors and Kontsevich's formality of the little balls operad. |
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