Results 1  10
of
15
Constructions with Bundle Gerbes
"... This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting applications in physics. i iiStatement ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead to some interesting applications in physics. i iiStatement of Originality This thesis contains no material which has been accepted for the award of any other degree or diploma at any other university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to this copy of my thesis, when deposited in the University Library, being made available for loan and photocopying. Stuart Johnson
Formal Homotopy Quantum Field Theories
 II : Simplicial Formal Maps
"... Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed dmanifolds endowed with extra structure in the form of homotopy classes of maps into a given ‘target ’ space. For d = 1, classifications of HQ ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed dmanifolds endowed with extra structure in the form of homotopy classes of maps into a given ‘target ’ space. For d = 1, classifications of HQFTs in terms of algebraic structures are known when B is a K(G,1) and also when it is simply connected. Here we study general HQFTs with d = 1 and target a general 2type, giving a common generalisation of the classifying algebraic structures for the two cases previously known. The algebraic models for 2types that we use are crossed modules, C, and we introduce a notion of formal Cmap, which extends the usual latticetype constructions to this setting. This leads to a classification of ‘formal ’ 2dimensional HQFTs with target C,
TQFT’s and gerbes
 Algebr. Geom. Topol
"... We generalise the notions of holonomy and parallel transport for abelian bundles and gerbes using an embedded TQFT construction, and obtain statesumlike formulae for the parallel transport along paths and surfaces. This approach has been greatly influenced by the work of Graeme Segal, in particula ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We generalise the notions of holonomy and parallel transport for abelian bundles and gerbes using an embedded TQFT construction, and obtain statesumlike formulae for the parallel transport along paths and surfaces. This approach has been greatly influenced by the work of Graeme Segal, in particular his axiomatic approach to Conformal Field Theory. 1
Homological Quantum Field Theory
 in M. Levy (Ed.), Mathematical Physics Research Developments, Nova Publishers
"... We show that the space of chains of smooth maps from spheres into a fixed compact oriented manifold has a natural structure of a transversal dalgebra. We construct a structure of transversal 1category on the space of chains of maps from a suspension space S(Y), with certain boundary restrictions, ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
We show that the space of chains of smooth maps from spheres into a fixed compact oriented manifold has a natural structure of a transversal dalgebra. We construct a structure of transversal 1category on the space of chains of maps from a suspension space S(Y), with certain boundary restrictions, into a fixed compact oriented manifold. We define homological quantum field theories HLQFT and construct several examples of such structures. Our definition is based on the notions of string topology of Chas and Sullivan, and homotopy quantum field theories of Turaev. 1
Relative differential Kcharacters
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2008
"... We define a group of relative differential Kcharacters associated with a smooth map between two smooth compact manifolds. We show that this group fits into a short exact sequence as in the nonrelative case. Some secondary geometric invariants are expressed in this theory. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We define a group of relative differential Kcharacters associated with a smooth map between two smooth compact manifolds. We show that this group fits into a short exact sequence as in the nonrelative case. Some secondary geometric invariants are expressed in this theory.
and
, 2008
"... We present a general framework for TQFT and related constructions using the language of monoidal categories. We construct a topological category C and an algebraic category D, both monoidal, and a TQFT functor is This work was supported by the programme “Programa Operacional Ciência, Tecnologia, Ino ..."
Abstract
 Add to MetaCart
We present a general framework for TQFT and related constructions using the language of monoidal categories. We construct a topological category C and an algebraic category D, both monoidal, and a TQFT functor is This work was supported by the programme “Programa Operacional Ciência, Tecnologia, Inovação ” (POCTI) of the Fundação para a Ciência e Tecnologia (FCT), cofinanced by the European Community fund FEDER. then defined as a certain type of monoidal functor from C to D. In contrast with the cobordism approach, this formulation of TQFT is closer in spirit to the classical functors of algebraic topology, like homology. The fundamental operation of gluing is incorporated at the level of the morphisms in the topological category through the notion of a gluing morphism, which we define. It allows not only the gluing together of two separate objects, but also the selfgluing of a single object to be treated in the same fashion. As an example of our framework we describe TQFT’s for oriented 2Dmanifolds, and classify a family of them in terms of a pair of tensors satisfying some relations.
A FUNCTORIAL APPROACH TO nGERBES
, 2002
"... Abstract. We provide a characterisation of ngerbes with connection in terms of a variant of Turaev’s homotopy quantum field theories based on chains in a smooth manifold X. ..."
Abstract
 Add to MetaCart
Abstract. We provide a characterisation of ngerbes with connection in terms of a variant of Turaev’s homotopy quantum field theories based on chains in a smooth manifold X.
ATG TQFT’s and gerbes
, 2004
"... Abstract We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes with connection that there is a onetoone correspon ..."
Abstract
 Add to MetaCart
Abstract We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes with connection that there is a onetoone correspondence between their local description in terms of locallydefined functions and forms and their nonlocal description in terms of a suitable class of embedded TQFT’s. AMS Classification 55R65; 53C29