51 research outputs found
On the delooping of (framed) embedding spaces
It is known that the bimodule derived mapping spaces between two operads have
a delooping in terms of the operadic mapping space. We show a relative version
of that statement. The result has applications to the spaces of disc embeddings
fixed near the boundary and framed disc embeddings.Comment: arXiv admin note: text overlap with arXiv:1704.0706
Projective and Reedy model category structures for (infinitesimal) bimodules over an operad
We construct and study projective and Reedy model category structures for
bimodules and infinitesimal bimodules over topological operads. Both model
structures produce the same homotopy categories. For the model categories in
question, we build explicit cofibrant and fibrant replacements. We show that
these categories are right proper and under some conditions left proper. We
also study the extension/restriction adjunctions.Comment: All comments on this work are welcom
Graph-complexes computing the rational homotopy of high dimensional analogues of spaces of long knots
Real Homotopy Theory of Semi-Algebraic Sets
We complete the details of a theory outlined by Kontsevich and Soibelman that
associates to a semi-algebraic set a certain graded commutative differential
algebra of "semi-algebraic differential forms" in a functorial way. This
algebra encodes the real homotopy type of the semi-algebraic set in the spirit
of the DeRham algebra of differential forms on a smooth manifold. Its
development is needed for Kontsevich's proof of the formality of the little
cubes operad.Comment: 58 pages. Cosmetic changes with respect to previous version.
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