It is shown how the deformation of the superconformal generators on the string’s worldsheet by a nonabelian super-Wilson line gives rise to a covariant exterior derivative on loop space coming from a nonabelian 2-form on target space. The expression obtained this way is new in the context of strings (but has been considered before in the context of integrable systems), and its consistency is ve...

Let M be an oriented manifold and let N be a set consisting of oriented closed manifolds of possibly different dimensions. Roughly speaking, the space GN,M of N-garlands in M is the space of mappings into M of singular manifolds obtained by gluing manifolds from N at some marked points. In our previous work with Rudyak we introduced a rich algebra structure on the bordism group Ω∗(GN,M ). In th...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

We study the Rouquier dimension of wrapped Fukaya categories Liouville manifolds and pairs, apply this invariant to various problems in algebraic symplectic geometry. On algebro-geometric side, we introduce a new method based on flexibility mirror symmetry bound derived coherent sheaves certain complex varieties stacks. These bounds are sharp at most $3$ . As an application, resolve well-known ...

The goal of this paper is to describe, in as much detail as possible, the structure of the algebra of differential invariants of a Lie pseudo-group. Under the assumption of local freeness of the prolonged pseudo-group action, we develop algorithms for locating a finite generating set of differential invariants, establishing the recurrence relations for the differentiated invariants, and fixing ...

Let M be a closed, oriented, n-manifold, and LM its free loop space. In [C-S1] a commutative algebra structure in homology, H∗(LM), and a Lie algebra structure in equivariant homology H 1 ∗ (LM), were defined. In this paper we prove that these structures are homotopy invariant for simply connected manifolds in the following sense. Let f : M1 → M2 be a homotopy equivalence of simply connected cl...

Let A ∈ GL(n,C) be a diagonal linear operator, with all eigenvalues satisfying |αi| < 1, and M = (Cn\0)/〈A〉 the corresponding Hopf manifold. We show that any stable holomorphic bundle on M can be lifted to a G̃F equivariant coherent sheaf on C, where G̃F ∼= (C) is a commutative Lie group acting on C and containing A. This is used to show that all stable bundles onM are filtrable, that is, admit a...

This is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In [3] we introduced the basic DG category PA• , the perfect category of A•, which corresponded to the category of coherent sheaves on a complex manifold. In this paper we enlarge this category to include objects which correspond to quasi-coherent ...