Chien‐Hao Liu

activity

19952025

most citedTarget Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level

22 citations · 221 across the 45 of their papers we have counts for

collaborators

Showing 2010Show all

2 papers · 1 filter

math.SG2010★ 5 cited

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 $C^{\infty}$ -manifolds with a fundamental module and morphisms therefrom to a complex manifold. In t…

math.SG2010★ 14 cited

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…