Related papers: Topological Terms in String Theory on Orbifolds
This note is about invariants of moduli spaces of curves. It includes their intersection theory and cohomology. Our main focus in on the distinguished piece containing the so called tautological classes. These are the most natural classes…
We study deformations of closed string theory by primary fields of conformal weight $(1,1)$, using conformal techniques on the complex plane. A canonical surface integral formalism for computing commutators in a non-holomorphic theory is…
We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen…
I present a new class of topological string theories, and discuss them in two dimensions as candidates for the string description of large-$N$ QCD. The starting point is a new class of topological sigma models, whose path integral is…
We construct the infinite sequence of invariants for curves in surfaces by using word theory that V. Turaev introduced. For plane closed curves, we add some extra terms, e.g. the rotation number. From these modified invariants, we get the…
We study topological string theory on elliptically fibered Calabi-Yau threefolds using mirror symmetry. We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the…
We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion…
We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact four-cycles, also referred to as strip geometries. We show that various quantities…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
We begin with the construction of Mathai-Quillen's Thom form. We also study the case with group actions, with a review of equivariant cohomology and then Mathai-Quillen's construction in this setting. Next, we show that much of the above…
We develop the real vertex formalism for the computation of the topological string partition function with D-branes and O-planes at the fixed point locus of an anti-holomorphic involution acting non-trivially on the toric diagram of any…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…
We propose a topological paradigm in alterfold topological quantum field theory to explore various concepts, including modular invariants, $\alpha$-induction and connections in Morita contexts within a modular fusion category of non-zero…
The paper explains the connection between topological theories for one-manifolds with defects and values in the Boolean semiring and automata and their generalizations. Finite state automata are closely related to regular languages. To each…
We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field…
We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…
This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
Using an imbedding supported background tensor approach for the differential geometry of an imbedded surface in an arbitrary background, we show that the topological terms associated with the inner and outer curvature scalars of the string…