Related papers: On the Classification of Topological Field Theorie…
We prove that smooth 1-dimensional topological field theories over a manifold are equivalent to vector bundles with connection. The main novelty is our definition of the smooth 1-dimensional bordism category, which encodes cutting laws…
We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.
Using methods inspired from algebraic $K$-theory, we give a new proof of the Genauer fibration sequence, relating the cobordism categories of closed manifolds with cobordism categories of manifolds with boundaries, and of the…
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in…
We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory. These spaces are: - Kazarian's space (generalizing Vassiliev's algebraic complex and) showing which cohomology classes are represented by…
It is shown that every algebraic quantum field theory has an underlying functorial field theory which is defined on a suitable globally hyperbolic Lorentzian bordism pseudo-category. This means that globally hyperbolic Lorentzian bordisms…
We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite…
We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor categories equipped with a square root of the global…
An equivariant topological field theory is defined on a cobordism category of manifolds with principal fiber bundles for a fixed (finite) structure group. We provide a geometric construction which for any given morphism $G \to H$ of finite…
The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over the rationals) of the corresponding cobordism groups over Spec(C) for all dimensions of varieties and…
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of…
A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby we classify these types of 2-dimensional extended topological…
This paper introduces a geometric framework for classical cohomological field theories based on $G^{\star}$-algebras and gauge natural field theories. A BV-BFV extension of the framework is provided, which incorporates the cotangent lift of…
The structure of topological quantum field theories on the compact Kahler manifold is interpreted. The BRST transformations of fields are derived from universal bundle and the observables are found from the second Chern class of universal…
Starting from the quantum group SL_q(2,C), we construct operator invariants of 3-cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the Reshetikhin--Turaev and Turaev--Viro models.…