Link Homology and Unoriented Topological Quantum Field Theory
نویسنده
چکیده
We investigate Khovanov homology of stable equivalence classes of link diagrams on oriented surfaces. We apply Bar-Natan’s geometric formalism to this setting and using unoriented 1+1-dimensional topological quantum field theories we define new link homology theories for stable equivalences classes.
منابع مشابه
Unoriented topological quantum field theory and link homology
In this paper we consider link diagrams on orientable surfaces up to the relation of stable equivalence, that is up to homeomorphisms of surfaces, Reidemeister moves and the addition or subtraction of handles disjoint from the diagram. Stable equivalence classes of link diagrams have an equivalent formulation in terms of so called “virtual” link diagrams pioneered by Kauffman (see for example t...
متن کاملEquivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases
Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented ...
متن کاملFactorization Homology of Stratified Spaces
This work forms a foundational study of factorization homology, or topological chiral homology, at the generality of stratified spaces with tangential structures. Examples of such factorization homology theories include intersection homology, compactly supported stratified mapping spaces, and Hochschild homology with coefficients. Our main theorem characterizes factorization homology theories b...
متن کاملNoncommutative Topological Quantum Field Theory-Noncommutative Floer Homology
We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology 3-spheres. There is also a physical motivation: one would like to construct a noncommutative topological quantum field theory. The two motivations are closely r...
متن کاملOpen and Unoriented Strings from Topological Membrane I. Prolegomena
We study the orbifold of Topological Membrane (TM), a Topological Massive Gauge Theory (TMGT), defined in S × [0, 1] and T 2 × [0, 1]. The orbifolding is constructed by gauging discrete symmetries of the bulk 3D field theory, namely PCT/PT symmetries. We consider several generalized definitions of parity, depending on these choices we obtain open, open unoriented and close unoriented theories. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005