22 citations · 221 across the 45 of their papers we have counts for
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D-branes and synthetic/-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifolds
Chien-Hao Liu, Shing-Tung Yau
We lay down an elementary yet fundamental lemma concerning a finite algebraicness property of a smooth map from an Azumaya/matrix manifold with a fundamental module to a smooth man…
D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck
Chien-Hao Liu, Shing-Tung Yau
In [L-Y5] (D(6): arXiv:1003.1178 [math.SG]) we introduced the notion of Azumaya -manifolds with a fundamental module and morphisms therefrom to a complex manifold. In t…
D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
Chien-Hao Liu, Shing-Tung Yau
We review first Azumaya geometry and D-branes in the realm of algebraic geometry along the line of Polchinski-Grothendieck Ansatz from our earlier work and then use it as backgroun…
Degeneration and gluing of Kuranishi structures in Gromov-Witten theory and the degeneration/gluing axioms for open Gromov-Witten invariants under a symplectic cut
Chien-Hao Liu, Shing-Tung Yau
We study the degeneration and the gluing of Kuranishi structures in Gromov-Witten theory under a symplectic cut. This leads us to a degeneration axiom and a gluing axiom for open G…