Results 11 to 20 of about 259 (35)

Universal manifold pairings and positivity [PDF]

, 2005
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p= with values in (formal linear combinations of) closed manifolds.
Akbulut, Akbulut, Alexei Kitaev, Atiyah, Casson, Chetan Nayak, Freedman, Freedman, Johannes K Slingerland, Kevin Walker, Kirby, Kirby, Matveyev, Michael H Freedman, Schubert, Zhenghan Wang   +15 more
core   +9 more sources

Generalized Legendre transformations and symmetries of the WDVV equations [PDF]

, 2016
The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class - the so-called Legendre transformations - were introduced by Dubrovin.
Stedman, Richard, Strachan, Ian A. B.
core   +2 more sources

Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes [PDF]

, 2012
The degree zero part of the quantum cohomology algebra of a smooth Fano toric symplectic manifold is determined by the superpotential function, W, of its moment polytope. In particular, this algebra is semisimple, i.e.
Alexander Givental, Benjamin Nill, Benjamin P. Mirabelli, D. McDuff, David Cox, Günter Ewald, J. Lagarias, K. Fukaya, M. Entov, Maksim Maydanskiy, Matthew Strom Borman, Michael Usher, Mikkel Obro, Robin Hartshorne, T. Delzant, W. Fulton, Wilhelm Ljunggren, William Fulton, Y. Eliashberg, Y. Ostrover, Yaron Ostrover   +20 more
core   +1 more source

Theory of Submanifolds, Associativity Equations in 2D Topological Quantum Field Theories, and Frobenius Manifolds

, 2006
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of ...
B. Dubrovin, O. I. Mokhov, O. I. Mokhov
core   +2 more sources

Logarithmic asymptotics of the genus zero Gromov-Witten invariants of the blown up plane

, 2005
We study the growth of the genus zero Gromov-Witten invariants GW_{nD} of the projective plane P^2_k blown up at k points (where D is a class in the second homology group of P^2_k).
Di Francesco, Eugenii Shustin, Greuel, Göttsche, Hofer, Ilia Itenberg, Kollár, Kontsevich, McDuff, McDuff, McDuff, Viatcheslav Kharlamov   +11 more
core   +5 more sources

On the injectivity radius in Hofer's geometry

, 2014
In this note we consider the following conjecture: given any closed symplectic manifold $M$, there is a sufficiently small real positive number $\rho$ such that the open ball of radius $\rho$ in the Hofer metric centered at the identity on the group of ...
Lalonde, François, Savelyev, Yakov
core   +1 more source

Worldsheet Instantons and Torsion Curves [PDF]

, 2008
We study aspects of worldsheet instantons relevant to a heterotic standard model. The non-simply connected Calabi-Yau threefold used admits Z_3 x Z_3 Wilson lines, and a more detailed investigation shows that the homology classes of curves are H_2(X,Z)=Z^
Braun, Volker, Kreuzer, Maximilian, Ovrut, Burt A., Scheidegger, Emanuel   +3 more
core   +1 more source

Frobenius 3-Folds via Singular Flat 3-Webs [PDF]

, 2012
We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1) the web germ ...
Agafonov, Sergey I.
core   +5 more sources

The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints [PDF]

, 2014
The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra.
van de Leur, Johan
core   +2 more sources

Multiple quantum products in toric varieties

, 2001
We generalize the author's formula for Gromov-Witten invariants of symplectic toric manifolds (see math.AG/0006156) to those needed to compute the quantum product of more than two classes directly, i.e.
Spielberg, Holger
core   +5 more sources