Results 11 to 20 of about 267 (35)

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

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

Minimal symplectic atlases of Hermitian symmetric spaces [PDF]

, 2015
In this paper we compute the minimal number of Darboux chart needed to cover a Hermitian symmetric space of compact type in terms of the degree of their embeddings in $\mathbb{C} P^N$. The proof is based on the recent work of Y. B. Rudyak and F. Schlenk [
Mossa, Roberto, Placini, Giovanni
core   +1 more source

Manifold Ways to Darboux-Halphen System [PDF]

, 2018
Many distinct problems give birth to Darboux-Halphen system of differential equations and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding infinite number of double ...
Morales, John Alexander Cruz, Movasati, Hossein, Nikdelan, Younes, Roychowdhury, Raju, Torres, Marcus A. C.   +4 more
core   +3 more sources

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   +7 more sources

Open WDVV equations and Frobenius structures for toric Calabi-Yau 3-folds

Forum of Mathematics, Sigma
Let X be a toric Calabi-Yau 3-fold and let $L\subset X$ be an Aganagic-Vafa outer brane. We prove two versions of open WDVV equations for the open Gromov-Witten theory of $(X,L)$ .
Song Yu, Zhengyu Zong
doaj   +1 more source

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   +6 more sources

A mirror theorem for Gromov-Witten theory without convexity

Forum of Mathematics, Sigma
We prove a genus zero Givental-style mirror theorem for all complete intersections in toric Deligne-Mumford stacks, which provides an explicit slice called big I-function on Givental’s Lagrangian cone for such targets.
Jun Wang
doaj   +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

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