65 citations · 195 across the 28 of their papers we have counts for
18 papers · 1 filter
Diagrams for primitive cycles in spaces of pure braids and string links
Rafal Komendarczyk, Robin Koytcheff, Ismar Volic
The based loop space of a configuration space of points in a Euclidean space can be viewed as a space of pure braids in a Euclidean space of one dimension higher. We continue our s…
Diagram complexes, formality, and configuration space integrals for braids
Rafal Komendarczyk, Robin Koytcheff, Ismar Volic
We use rational formality of configuration spaces and the bar construction to study the cohomology of the space of braids in dimension four or greater. We provide a diagram complex…
A streamlined proof of the convergence of the Taylor tower for embeddings in
Franjo Sarcevic, Ismar Volic
Manifold calculus of functors has in recent years been successfully used in the study of the topology of various spaces of embeddings of one manifold in another. Given a space of e…
Low stages of the Taylor tower for r-immersions
Bridget Schreiner, Franjo Sarcevic, Ismar Volic
We study the beginning of the Taylor tower, supplied by manifold calculus of functors, for the space of r-immersions, which are immersions without r-fold self-intersections. We des…
Functors between Reedy model categories of diagrams
Philip S. Hirschhorn, Ismar Volic
If is a Reedy category and is a model category, the category of -diagrams in is a model category under the Reedy model category structure. If is a…
Milnor invariants of string links, trivalent trees, and configuration space integrals
Robin Koytcheff, Ismar Volic
We study configuration space integral formulas for Milnor's homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. O…
Configuration space integrals and the cohomology of the space of homotopy string links
Robin Koytcheff, Brian A. Munson, Ismar Volic
Configuration space integrals have in recent years been used for studying the cohomology of spaces of (string) knots and links in for since they provide a map…
On the cohomology of spaces of links and braids via configuration space integrals
Ismar Volic
We study the cohomology of spaces of string links and braids in for using configuration space integrals. For , these integrals give a chain map from c…
Cosimplicial models for spaces of links
Brian A. Munson, Ismar Volic
We study the spaces of string links and homotopy string links in an arbitrary manifold using multivariable manifold calculus of functors. We construct multi-cosimplicial models for…
Multivariable manifold calculus of functors
Brian A. Munson, Ismar Volic
Manifold calculus of functors, due to M. Weiss, studies contravariant functors from the poset of open subsets of a smooth manifold to topological spaces. We introduce "multivariabl…
Formality of the little N-disks operad
Pascal Lambrechts, Ismar Volic
We develop the details of Kontsevich's proof of the formality of little N-disks operad over the field of real numbers. Formality holds in the category of operads of chain complexes…
Real Homotopy Theory of Semi-Algebraic Sets
Robert Hardt, Pascal Lambrechts, Victor Tourtchine +1
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-algebrai…
The rational homology of spaces of long knots in codimension >2
Pascal Lambrechts, Victor Tourtchine, Ismar Volic
We determine the rational homology of the space of long knots in R^d for . Our main result is that the Vassiliev spectral sequence computing this rational homology collapse…
Coformality and the rational homotopy groups of spaces of long knots
Gregory Arone, Pascal Lambrechts, Victor Tourtchine +1
We show that the Bousfield-Kan spectral sequence which computes the rational homotopy groups of the space of long knots in , where , collapses at the p…
Associahedron, cyclohedron, and permutohedron as compactifications of configuration spaces
P. Lambrechts, V. Tourtchine, I. Volic
As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or o…
Calculus of functors, operad formality, and rational homology of embedding spaces
Gregory Arone, Pascal Lambrechts, Ismar Volic
Let M be a smooth manifold and V a Euclidean space. Let Ebar(M,V) be the homotopy fiber of the map from Emb(M,V) to Imm(M,V). This paper is about the rational homology of Ebar(M,V)…
Calculus of the embedding functor and spaces of knots
Ismar Volic
We give an overview of how calculus of the embedding functor can be used for the study of long knots and summarize various results connecting the calculus approach to the rational…
Finite type knot invariants and calculus of functors
Ismar Volic
We associate a Taylor tower supplied by calculus of the embedding functor to the space of long knots and study its cohomology spectral sequence. The combinatorics of the spectral s…