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THE ACTION OF THE MAPPING CLASS GROUP ON REPRESENTATION VARIETIES
MAPPING CLASS GROUP REPRESENTATION VARIETIES
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2015/12/17
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...
ERGODICITY OF MAPPING CLASS GROUP ACTIONS ON SU(2)-CHARACTER VAR IET IES
GROUP ACTIONS MAPPING CLASS
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2015/9/29
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)-...
THE MAPPING CLASS GROUP ACTS REDUCIBLY ON SU(n)-CHARACTER VARIETIES
CLASS GROUP ACTS REDUCIBLY VARIETIES
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2015/9/29
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
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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...
A Short Note on Mapping Cylinders
A Short Note Mapping Cylinders Algebraic Topology
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2012/6/25
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.
Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifolds
Homological eigenvalues mapping classes torsion homology growth fibered 3--manifolds Group Theory
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2012/5/9
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...
On visualization of the linearity problem for mapping class groups of surfaces
visualization linearity problem mapping class groups surfaces
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2012/3/1
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...
The Hessenberg matrix and the Riemann mapping
Hessenberg matrix Riemann mapping Spectral Theory
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2011/9/29
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...
The Witten-Reshetikhin-Turaev invariants of finite order mapping tori II
The Witten-Reshetikhin-Turaev invariants finite order mapping tori II Geometric Topology
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2011/8/31
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...
Conformal Mapping of Circular Quadrilaterals and Weierstrass Elliptic Functions
conformal mapping accessory parameter Schwarzian derivative
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2011/2/21
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.
A faithful linear-categorical action of the mapping class group of a surface with boundary
faithful linear-categorical action mapping class group surface with boundary
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2011/1/18
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 ...
Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
$D_N$ type quantum Calogero model through free harmonic oscillators
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2011/3/3
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...
Simply Intersecting Pair Maps in the Mapping Class Group
Pair Maps Mapping Class Group
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2011/2/24
The Torelli group, I(Sg), is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface.
Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
Exact solution of $D_N$ type quantum Calogero model mapping to free harmonic oscillators
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2010/12/28
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...
New series in the Johnson cokernels of the mapping class groups of surfaces
New series Johnson cokernels mapping class groups of surfaces
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2011/1/20
Let g,1 be a compact oriented surface of genus g with one boundary component,andMg,1 its mapping class group. Morita showed that the image of the k-th Johnson homomorphism M
k of Mg,1 is contained ...