Results 1  10
of
39
Manifoldtheoretic compactifications of configuration spaces
 Selecta Math. (N.S
"... Abstract. We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to FultonMacPherson and AxelrodSinger in the setting of smooth manifolds, as well as a simplicial variant of this compactification. Our constructions are elemen ..."
Abstract

Cited by 23 (5 self)
 Add to MetaCart
Abstract. We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to FultonMacPherson and AxelrodSinger in the setting of smooth manifolds, as well as a simplicial variant of this compactification. Our constructions are elementary and give simple global coordinates for the compactified configuration space of a general manifold embedded in Euclidean space. We stratify the canonical compactification, identifying the diffeomorphism types of the strata in terms of spaces of configurations in the tangent bundle, and give completely explicit local coordinates around the strata as needed to define a manifold with corners. We analyze the quotient map from the canonical to the simplicial compactification, showing it is a homotopy equivalence. We define projection maps and diagonal maps, which for the simplicial variant satisfy cosimplicial identities.
Higherdimensional BF theories in the BatalinVilkovisky formalism: The BV action and generalized Wilson loops
 math.QA/0010172 THE AKSZ FORMULATION OF THE POISSON SIGMA MODEL 19
"... ABSTRACT. This paper analyzes in details the Batalin–Vilkovisky quantization procedure for BF theories on ndimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular, generalized Wilson loops for BF theories with addit ..."
Abstract

Cited by 17 (9 self)
 Add to MetaCart
ABSTRACT. This paper analyzes in details the Batalin–Vilkovisky quantization procedure for BF theories on ndimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular, generalized Wilson loops for BF theories with additional polynomial Binteractions are discussed in any dimensions. The paper also contains the explicit proofs to the Theorems stated in [16].
Algebraic structures on graph cohomology
 J. of Knot Theory and its Ramifications
"... Abstract. We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S 1 or R into R n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb (S 1, R n) whe ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
Abstract. We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S 1 or R into R n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb (S 1, R n) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in R 3. 1.
Rossi: “Loop observables for BF theories in any dimension and the cohomology of knots
, 2000
"... ABSTRACT. A generalization of Wilson loop observables for BF theories in any dimension is introduced in the Batalin–Vilkovisky framework. The expectation values of these observables are cohomology classes of the space of imbeddings of a circle. One of the resulting theories discussed in the paper ha ..."
Abstract

Cited by 9 (7 self)
 Add to MetaCart
ABSTRACT. A generalization of Wilson loop observables for BF theories in any dimension is introduced in the Batalin–Vilkovisky framework. The expectation values of these observables are cohomology classes of the space of imbeddings of a circle. One of the resulting theories discussed in the paper has only trivalent interactions and, irrespective of the actual dimension, looks like a 3dimensional Chern–Simons theory. 1.
The rational homology of the space of long knots in codimension greater than two, preprint
"... Abstract. We determine the rational homology of the space of long knots in R d for d ≥ 4. Our main result is that the Vassiliev spectral sequence computing this rational homology collapses at the E 1 page. As a corollary we get that the homology of long knots (modulo immersions) is the Hochschild ho ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Abstract. We determine the rational homology of the space of long knots in R d for d ≥ 4. Our main result is that the Vassiliev spectral sequence computing this rational homology collapses at the E 1 page. As a corollary we get that the homology of long knots (modulo immersions) is the Hochschild homology of the Poisson algebras operad with a bracket of degree d −1, which can be obtained as the homology of an explicit graph complex and is in theory completely computable. Our proof is a combination of a relative version of Kontsevich’s formality of the little ddisks operad and of Sinha’s cosimplicial model for the space of long knots arising from GoodwillieWeiss embedding calculus. As another ingredient in our proof, we introduce a generalization of a construction that associates a cosimplicial object to a multiplicative operad. Along the way we also establish some results about the BousfieldKan spectral sequences of a truncated cosimplicial space. 1.
Configuration space integrals and Taylor towers for spaces of knots. Submitted
, 2004
"... Abstract. We describe Taylor towers for spaces of knots arising from Goodwillie’s calculus of functors and extend the configuration space integrals of Bott and Taubes from spaces of knots to the stages of the towers. We prove the vanishing results in detail to show that certain combinations of integ ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. We describe Taylor towers for spaces of knots arising from Goodwillie’s calculus of functors and extend the configuration space integrals of Bott and Taubes from spaces of knots to the stages of the towers. We prove the vanishing results in detail to show that certain combinations of integrals, dictated by trivalent diagrams, yield cohomology classes of the stages of the tower, just as they do for ordinary knots. We then use this factorization of BottTaubes integrals through the Taylor tower to deduce a vanishing result for a spectral sequence converging to the cohomology of spaces of knots. We also give another proof of the wellknown result that BottTaubes integrals combine to yield a universal finite type knot invariant. 1.
surfaces and higher dimensional knot invariants, Commun.Math.Phys
 Categorical Geometry and the Mathematical Foundations of Quantum General Relativity; Contribution to the Cambridge University Press volume on Quantum Gravity
, 2006
"... Abstract. An observable for nonabelian, higherdimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higherdimensional knots. 1. ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. An observable for nonabelian, higherdimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higherdimensional knots. 1.
HOMOTOPY GRAPHCOMPLEX FOR CONFIGURATION AND KNOT SPACES
, 2006
"... Abstract. In the paper we prove that the primitive part of the Sinha homology spectral sequence E 2term for the space of long knots is rationally isomorphic to the homotopy E 2term. We also define natural graphcomplexes computing the rational homotopy of configuration and of knot spaces. 1. ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. In the paper we prove that the primitive part of the Sinha homology spectral sequence E 2term for the space of long knots is rationally isomorphic to the homotopy E 2term. We also define natural graphcomplexes computing the rational homotopy of configuration and of knot spaces. 1.
3.1.
"... Abstract. Simplicial and ∆structures of configuration spaces are investigated. New connections between the homotopy groups of the 2sphere and the braid groups are given. The higher homotopy groups of the 2 sphere are shown to be derived groups of the braid groups over the 2sphere. Moreover the h ..."
Abstract
 Add to MetaCart
Abstract. Simplicial and ∆structures of configuration spaces are investigated. New connections between the homotopy groups of the 2sphere and the braid groups are given. The higher homotopy groups of the 2 sphere are shown to be derived groups of the braid groups over the 2sphere. Moreover the higher homotopy groups of the 2sphere are shown to be isomorphic to the