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Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture
Parametrized Ring-Spectra the Nearby Lagrangian Conjecture Symplectic Geometry
2011/9/19
Abstract: We prove that any closed connected exact Lagrangian manifold L in a connected cotangent bundle T*N is up to a finite covering space lift a homology equivalence. We prove this by constructing...
Knot state asymptotics II, Witten conjecture and irreducible representations
Knot state asymptotics II Witten conjecture irreducible representations Geometric Topology
2011/8/30
Abstract: This article pursues the study of the knot state asymptotics in the large level limit initiated in "Knot sate Asymptotics I". As a main result, we prove the Witten asymptotic expansion conje...
Knot state asymptotics I, AJ Conjecture and abelian representations
Knot state asymptotics I AJ Conjecture abelian representations Geometric Topology
2011/8/30
Abstract: Consider the Chern-Simons topological quantum field theory with gauge group SU(2) and level k. Given a knot in the 3-sphere, this theory associates to the knot exterior an element in a vecto...
On the homological mirror symmetry conjecture for pairs of pants
homological mirror symmetry pairs of pants
2011/2/21
The n-dimensional pair of pants is defined to be the complement of n + 2 generic hyperplanes in CPn. We construct an immersed Lagrangian sphere in the pair of pants and compute its endomorphism A∞ alg...