Results 1 
8 of
8
Homotopy Gerstenhaber algebras
 OF SCIENCES OF THE CZECH REPUBLIC MATHEMATICAL INSTITUTE
, 2000
"... Dedicated to the memory of Moshé Flato Abstract. The purpose of this paper is to complete GetzlerJones ’ proof of Deligne’s Conjecture, thereby establishing an explicit relationship between the geometry of configurations of points in the plane and the Hochschild complex of an associative algebra. M ..."
Abstract

Cited by 19 (0 self)
 Add to MetaCart
Dedicated to the memory of Moshé Flato Abstract. The purpose of this paper is to complete GetzlerJones ’ proof of Deligne’s Conjecture, thereby establishing an explicit relationship between the geometry of configurations of points in the plane and the Hochschild complex of an associative algebra. More concretely, it is shown that the B∞operad, which is generated by multilinear operations known to act on the Hochschild complex, is a quotient of a certain operad associated to the compactified configuration spaces. Different notions of homotopy Gerstenhaber algebras are discussed: One of them is a B∞algebra, another, called a homotopy Galgebra, is a particular case of a B∞algebra, the others, a G∞algebra, an E 1algebra, and a weak G∞algebra, arise from the geometry of configuration spaces. Corrections to the paper of Kimura, Zuckerman, and the author related to the use of a nonextant notion of a homotopy Gerstenhaber algebra are made. In an unpublished paper of E. Getzler and J. D. S. Jones [GJ94], the notion of a homotopy nalgebra was introduced. Unfortunately the construction that justified
Hochschild cohomology and moduli spaces of strongly homotopy associative algebras
 Homology Homotopy Appl
"... Abstract. Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a twocell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of invertible power series acting on a certain space. The Hoc ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
Abstract. Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a twocell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of invertible power series acting on a certain space. The Hochschild cohomology rings of resulting A∞algebras have an interpretation as totally ramified extensions of discrete valuation rings. All A∞algebras are supposed to be unital and we give a detailed analysis of unital structures which is of independent interest. Keywords: A∞algebra, derivation, Hochschild cohomology, formal power series. 1.
What do dgcategories form
 Compositio Math
"... It is well known that categories form a 2category: 1arrows are functors and 2arrows are their natural transformations. In a similar way, dgcategories also form a 2category: 1arrows A → B are dgfunctors; given a pair of dgfunctors F,G: A → B one can define a complex of their natural transform ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
It is well known that categories form a 2category: 1arrows are functors and 2arrows are their natural transformations. In a similar way, dgcategories also form a 2category: 1arrows A → B are dgfunctors; given a pair of dgfunctors F,G: A → B one can define a complex of their natural transformations
Cochain operations defining Steenrod ⌣iproducts in the bar construction
 Georgian Math. J
"... the bar construction ..."
LATTICE GAUGE FIELD THEORY
, 2001
"... The inspiration for this thesis comes from mathematical physics, especially path integrals and the ChernSimons action. Path integrals were introduced by Feynman in late 1940’s and they have recently been applied to purely geometric problems. The work [33] of Edward Witten on the topological quantum ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The inspiration for this thesis comes from mathematical physics, especially path integrals and the ChernSimons action. Path integrals were introduced by Feynman in late 1940’s and they have recently been applied to purely geometric problems. The work [33] of Edward Witten on the topological quantum field theory has been found very attractive by many enthusiastic
The topology of spaces of knots
, 2003
"... We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of mapping spaces and another which is cosimplicial. At the geometric heart of these constructions is the evaluation map, used elsewhere for e ..."
Abstract
 Add to MetaCart
We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of mapping spaces and another which is cosimplicial. At the geometric heart of these constructions is the evaluation map, used elsewhere for example to define linking number and BottTaubes integrals. Our models are weakly homotopy equivalent to the corresponding knot spaces when the dimension of the ambient manifold is greater than three. There are spectral sequences with identifiable E¹ terms which converge to their cohomology and homotopy groups.