Related papers: The cobordism hypothesis
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
We extend the derived Algebraic bordism of Lowrey and Sch\"urg to a bivariant theory in the sense of Fulton and MacPherson, and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings…
We define Homotopy quantum field theories (HQFT) as Topological quantum field theories (TQFT) for manifolds endowed with extra structure in the form of a map into some background space X. We also build the category of homotopy cobordisms…
Topological quantum field theories (TQFTs) are symmetric monoidal functors out of cobordism categories. In dimension two, oriented TQFTs are famously classified by commutative Frobenius algebras. In the unoriented setting, the…
We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.
Cobordism categories have played an important role in classical geometry and more recently in mathematical treatments of quantum field theory. Here we will compute localisations of two-dimensional discrete cobordism categories. This allows…
This is an expository paper discussing various versions of Khovanov homology theories, interrelations between them, their properties, and their applications to other areas of knot theory and low-dimensional topology.
We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit…
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce some basic notions of Topological Quantum…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead…
We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features 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…
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…