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ACTION OF THE JOHNSON-TORELLI GROUP ON REPRESENTATION VARIETIES
JOHNSON-TORELLI mapping class group
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2015/9/29
Let Σ be a compact orientable surface with genus g and n boundary components B = (B1,...,Bn). Let c = (c1,...,cn) ∈ [−2,2]n. Then the
mapping class group MCG of Σ acts on the relative SU(2)-cha...
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)-...
NOTES ON A PAPER OF MESS
NOTES PAPER OF MESS
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2015/9/29
In his 1990 paper “Lorentz Spacetimes of Constant Curvature” [82], Geoff Mess
offered what was, at the time, a completely new approach to the study of spacetimes in 2 + 1-dimensions, prim...
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.
RECURRENT GEODESICS IN FLAT LORENTZ 3-MANIFOLDS
LORENTZ 3-MANIFOLDS GEODESICS
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2015/9/29
We introduce the notion of recurrent geodesic rays in
a complete °at Lorentz 3-manifold. We completely classify the
dynamical behavior of geodesics in cyclic quotients, and apply this
classiˉcation...
The Margulis Invariant of Isometric Actions on Minkowski (2+1)-Space
Minkowski (2+1)-Space Isometric Actions
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2015/9/29
Let E denote an a±ne space modelled on Minkowski (2+1)-space E
and let ¡ be a group of isometries whose linear part L(¡) is a purely hyperbolic
subgroup of SO0
(2;1). Margulis has deˉned ...
Affine Schottky Groups and Crooked Tilings
Affi ne Schottky Groups Crooked Tilings
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2015/9/29
In his doctoral thesis [3] and subsequent papers [4, 5], Todd Drumm developed
a theory of fundamental domains for discrete groups of isometries of Minkowski
(2 + 1)-space E, using polyhedra called c...
CONVEX REAL PROJECTIVE STRUCTURES ON CLOSED SURFACES ARE CLOSED
REAL PROJECTIVE STRUCTURES CLOSED SURFACES
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2015/9/29
T. The deformation space t(E) of convex Rp2_ structures on a closed
surface Y with X(z) < 0 is closed in the space Hom(7r, SL(3, IR))/SL(3, IR)
of equivalence classes of representations r1 (l) -- ...
The Symplectic Nature of Fundamental Groups of Surfaces
Surfaces Symplectic Nature
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2015/9/29
A symplectic structure on a manifold is a closed nondegenerate exterior 2-
form. The most common type of symplectic structure arises on a complex
manifold as the imaginary part of a Hermitian metr...
THE RADIANCE OBSTRUCTION AND PARALLEL FORMS ON AFFINE MANIFOLDS
RADIANCE OBSTRUCTION PARALLEL FORMS
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2015/9/29
A manifold M is affine if it is endowed with a distinguished atlas whose
coordinate changes are locally affine. When they are locally linear M is called
radiant. The obstruction to radiance is a o...
Three-Dimensional Affine Crystallographic Groupd
Affine Crystallographic Groupd affine
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2015/9/29
Those groups r which act properly discontinuously and aillnely on II?’ with
compact fundamental domain are classified. First it is shown that such a group f
contains a solvable subgroup of finite ...
TWO EXAMPLES OF AFFINE MANIFOLDS
AFFINE MANIFOLDS affine
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2015/9/29
An affine manifold is a manifold with a distinguished
system of affine coordinates, namely, an open covering by
charts which map homeomorphically onto open sets in an
affine space E such that on ov...
On the Polynomial Cohomology of Affine Manifolds
Affine Manifolds Polynomial Cohomology
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2015/9/29
It is well known that the real cohomology of a compact Riemannian manifold
M is isomorphic to the algebra of its harmonic forms. When M is a fiat
Riemannian manifold, i.e. a Euclidean manifold, a ...
A Generalization of Bieberbach's Theorem
Bieberbach's Theorem More precisely
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2015/9/29
In 1912 Bieberbach proved that every compact flat Riemannian manifold M is
finitely covered by a flat torus. More precisely, M has the form (F\G)/H where
G is a group of translations of Euclidean ...
Afflne manilolds with nilpotent holonomy
nilpotent holonomy affine
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2015/9/29
An affine manifold is a differentiable manifold together with an atlas of
coordinate charts whose coordinate changes extend to affine automorphisms of
Euclidean space. These charts are called atli...