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Search Results Results 1 -3 of 3. Springer, Softcover reprint of hardcover 2. Let P be a projective bundle with structure group PU n , i. This follows from the commutative diagram. We will first give a definition in terms of Fredholm operators, and then provide some equivalent, but more geometric definitions. Let H be a Z 2 -graded Hilbert space.
Then we can construct an associated bundle Fred 0 P whose fibres are Fred 0 H. We define the twisted K-theory group of the pair X, P to be the group of homotopy classes of maps. Let us now describe some other models for twisted K-theory which will be useful in our physical applications later on. A definition in algebraic K-theory may given as follows. A bundle of projective spaces P yields a bundle End P of algebras. Instead, we will work with the Banach algebra K H of compact operators on H with the norm topology.secbiterworar.tk
Categories, Bundles And Space Time Topology (Shiva Mathematics Series)
We will also need a smooth version of this definition. Finally, we propose a general definition based on K-theory with coefficients in a sheaf of rings. It parallels the bundle gerbe approach to twisted K-theory. Let B be a Banach algebra over C. Using the functor in the usual way, for X an equivalence of additive categories. The equivalence of categories ensures that there is a natural isomorphism of groups. Abstract: Non-linear existence problems can attacked with topological methods.
For example a map between closed manifolds of the same dimension is surjective if the degree is non-zero. The degree is a homotopy invariant and two mappings into the sphere are homotopic if and only if the degrees are equal. Framed cobordism is a generalization for maps between closed manifolds of different dimensions. Again homotopy classes into the sphere are fully captured by the Framed cobordism class.
In this talk I will discuss joint work with Alberto Abbondandolo in which we generalize the theory to an infinite dimensional setting. They proved the faithfulness of this action through the study of curves in a punctured disk while Burau representation is not faithful for braids with five strands or more. The work of Khovanov and Seidel also had a symplectic aspect that we now generalize. In this talk, I will explain the strategy and tools to get a symplectic monodromy in our case and prove its injectivity.
If time permits, I will explain how this action lifts to a symplectic categorical representation on a Fukaya category that should be related to the algebraic categorical representation. This is joint work with Tyrone Cutler. In this talk, I will explain how to construct a product structure on it. This product recovers the cup product on singular cohomology when we consider a Lagrangian filling of a Legendrian. Moreover, we show that this product is mapped to the product on Legendrian contact cohomology by a quasi-isomorphism from the Floer complex to the Legendrian contact cohomology complex defined in [CDRGG].
Finally, we can define higher order maps to extend the product resp. A-infinity functor. Title: Bauer-Furuta invariants. Title: Convex hypersurface theory 2. Based on joint work with Ko Honda.
Title: Skein valued Gromov-Witten invariants, large N duality, and refinement. Abstract: We define open Gromov-Witten invariants with values in the framed skein module and use them to prove large N duality and give a geometric definition of refined HOMFLY polynomials. Abstract: A formal step in the construction of a Floer homotopy type is the passage from flow categories to stable homotopy types.
Cohen-Jones-Segal gave a description of this via iterated Pontryagin-Thom constructions. I will explain a reformulation of this construction which is more amenable to considering general cohomology theories. This is joint work with A. Abstract: A fullness conjecture of Kuznetsov says that if a smooth projective variety X admits a full exceptional collection of line bundles of length l, then any exceptional collection of line bundles of length l is full.
Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such X. This is joint work with T. Ekholm and D. Abstract: Giroux proved that any Lagrangian embedding has a generating family if and only if its stable Gauss map is trivial. In this talk I will sketch a proof that all Lagrangians with stably trivial Gauss map actually has a generating family with fiberwise compact set of gradient trajectories this is very similar to having a g. Title: A Novikov fundamental group. Gadbled and H. Title: On the space of Legendrians isotopic to the zero section in Jet-1 bundles.
We show that under some assumptions, it is possible to write the superpotentials of the lifted Lagrangians in terms of the superpotentials of the original Lagrangians we may also need additional information coming from relative Gromov-Witten invariants. The superpotential of a Lagrangian is a count of pseudoholomorphic disks of Maslov index 2 with boundary on the Lagrangian, and it plays an important role in Floer theory and mirror symmetry. We will discuss applications of this result, including how it can be used to distinguish infinitely many monotone Lagrangian tori in complex projective planes, quadrics and cubics of complex dimension at least 3.
This is joint work with D. Tonkonog, R. Vianna and W. Abstract: Knot invariants can be defined using Legendrian isotopy invariants of the knot conormal. There are two types of invariants raised in this way: one is the knot contact differential graded algebra together with augmentations associated to this dga, and the other one is the category of simple sheaves microsupported along the knot conormal.
Nadler-Zaslow correspondence suggests a connection between the two types of invariants. I will present a classification result of simple sheaves, and relate it to KCH representations and two-variable augmentation polynomials. I will also present a Radon transform for sheaf categories, and explain how it corresponds to the specialization of Q on the sheaf side. There is a map from this SFT into string topology of the manifold.
I will show that, when K is a fibred knot i. I will also discuss some potential applications of this isomorphism. This is a work in progress in collaboration with Gilberto Spano. Title: The wrapped Fukaya category of a Weinstein manifold is generated by the cocores of the critical Weinstein handles. Abstract: We decompose any object in the wrapped Fukaya category of a 2n-dimensional Weinstein manifold as a twisted complex built from the cocores of the n-dimensional handles in a Weinstein handle decomposition.
Title: Refined curve counting and the tropical vertex group Abstract: The tropical vertex group of Kontsevich and Soibelman is generated by formal symplectomorphisms of the 2-dimensional algebraic torus. It plays a role in many problems in algebraic geometry and mathematical physics. Based on the tropical vertex group, Gross, Pandharipande and Siebert introduced an interesting Gromov-Witten theory on weighted projective planes which admits a very special expansion in terms of tropical counts.
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