287 research outputs found
From maps between coloured operads to Swiss-Cheese algebras
In the present work, we extract pairs of topological spaces from maps between
coloured operads. We prove that those pairs are weakly equivalent to explicit
algebras over the one dimensional Swiss-Cheese operad SC_{1}. Thereafter, we
show that the pair formed by the space of long knots and the polynomial
approximation of (k)-immerions from R^{d} to R^{n} is an SC_{d+1}-algebra
assuming the Dwyer-Hess'conjecture
On Operadic Actions on Spaces of Knots and 2-Links
In the present work, we realize the space of string 2-links as
a free algebra over a colored operad denoted (for "Swiss-Cheese
for links"). This result extends works of Burke and Koytcheff about the
quotient of by its center and is compatible with Budney's
freeness theorem for long knots. From an algebraic point of view, our main
result refines Blaire, Burke and Koytcheff's theorem on the monoid of isotopy
classes of string links. Topologically, it expresses the homotopy type of the
isotopy class of a string 2-link in terms of the homotopy types of the classes
of its prime factors.Comment: Comments are welcom
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
A model for configuration spaces of points
The configuration space of points on a -dimensional smooth framed manifold
may be compactified so as to admit a right action over the framed little
-disks operad. We construct a real combinatorial model for these modules,
for compact smooth manifolds without boundary
Delooping the functor calculus tower
We study a connection between mapping spaces of bimodules and of infinitesimal bimodules over an operad. As main application and motivation of our work, we produce an explicit delooping of the manifold calculus tower associated to the space of smooth maps of discs, , avoiding any given multisingularity and coinciding with the standard inclusion near . In particular, we give a new proof of the delooping of the space of disc embeddings in terms of little discs operads maps with the advantage that it can be applied to more general mapping spaces
Boardman-Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules
We develop the combinatorics of leveled trees in order to construct explicit resolutions of (co)operads and (co)operadic (co)bimodules. We build explicit cofibrant resolutions of operads and operadic bimodules in spectra analogous to the ordinary Boardman--Vogt resolutions and we express them as cobar constructions of indecomposable elements. Dually, in the context of CDGAs, we perform similar constructions, and we obtain fibrant resolutions of Hopf cooperads and Hopf cooperadic cobimodules. We also express them as bar constructions of primitive elements
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
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