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Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
The 1st Asian Pacific Conference on Concept Mapping (CMC-AP 2017) will take place in Beijing, China from Sept 20-22, 2017.The theme for CMC-AP 2017 will be Learning for Understanding the World and Our...
The 1st Asian Pacific Conference on Concept Mapping (CMC-AP 2017) will take place in Beijing, China from Sept 20-22, 2017.The theme for CMC-AP 2017 will be Learning for Understanding the World and Our...
These notes are based on lectures given at Zhejiang University, July 14–20, 2008. My goal was to present some analytic techniques that can be used to study the action of the mapping class group on the...
Let be a compact orientable surface with genus g andnboundary components ∂1,..., ∂n. Let b = (b1,...,bn) ∈ [−2,2] n. Then the mapping class group Mod() acts on the relative SU(2)-...
When G is a connected compact Lie group, and π is a closed surface group, then Hom(π, G)/G contains an open dense Out(π)-invariant subset which is a smooth symplectic manifold.
SET MAPPING REFLECTION     MAPPING REFLECTION       2015/8/17
The goal of these lectures is to give an exposition of the concept of an open stationary set, an associated reflection principle (for lack of a better word), and a list of examples of how this sort of...
Given a homotopy equivalence f between two topological spaces we obtain an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.
Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on th...
We derive two types of linearity conditions for mapping class groups of orientable surfaces; one for once-punctured surface, and the other for closed surface, respectively. For the once-punctured case...
Abstract: We show in this paper that, if \mu is a regular measure whose support is a Jordan arc or a connected finite union of Jordan arcs in the complex plane \mathbb{C}, then the limits of the eleme...
Abstract: We identify the leading order term of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-c...
Numerical and theoretical aspects of conformal mappings from a disk to a circular-arc quadrilateral, symmetric with respect to the coordinate axes, are devel-oped.
We show that the action of the mapping class group on bordered Floer homology in the second to extremal spinc-structure is faithful. The paper is self-contained, and in particular does not assume any ...
We solve the eigenvalue problem of the DN type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation.In particular, we construct the ei...

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