On the rational homology of high dimensional analogues of spaces of long knots

Details On the rational homology of high dimensional analogues of spaces of long knots On the rational homology of high dimensional analogues of spaces of long knots

2011-05-09

arxiv.org/abs/1105.1576v3

Mathematics

Algebraic Topology

Added a few references. Corrected a few misprints. Worked to improve the exposition

Scientific paper

We study high-dimensional analogues of spaces of long knots. These are spaces of compactly-supported embeddings between Euclidean spaces (modulo immersions). We show that when the dimensions are in the stable range, the rational homology groups of these spaces of embeddings can be calculated as the homology of a direct sum of certain finite chain complexes, which we describe rather explicitly. The proof uses the calculus of embeddings, the theory of operads, and some homological algebra of diagrams.

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