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THE PUZZLE CONJECTURE FOR THE COHOMOLOGY OF TWO-STEP FLAG MANIFOLDS
PUZZLE CONJECTURE TWO-STEP FLAG MANIFOLDS
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2015/12/17
We prove a conjecture of Knutson asserting that the Schubert
structure constants of the cohomology ring of a two-step flag variety are equal
to the number of puzzles with specified borde...
ANALYTIC CYCLES,BOTT-CHERN FORMS,AND SINGULAR SETS FOR THE YANG-MILLS FLOW ON KAHLER MANIFOLDS
BOTT-CHERN FORMS SINGULAR SETS YANG-MILLS FLOW KAHLER MANIFOLDS
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2015/12/17
It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact K¨ahler manifolds is completely determined by the Harder-NarasimhanSeshadri filtration of ...
TOPOLOGICAL SYMMETRY GROUPS OF GRAPHS IN 3-MANIFOLDS
GRAPHS IN 3-MANIFOLDS SYMMETRY GROUPS
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2015/12/17
We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group An which is not
the topological symmetry group of any graph embedded in the manifold.
...
THE COMPLEX VOLUME OF SL(n, C)-REPRESENTATIONS OF 3-MANIFOLDS
COMPLEX VOLUME 3-MANIFOLDS
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2015/12/17
For a compact 3-manifold M with arbitrary (possibly empty) boundary, we give a
parametrization of the set of conjugacy classes of boundary-unipotent representations of π1(M)
into SL(n, C). Our param...
GLUING EQUATIONS FOR PGL(n; C)-REPRESENTATIONS OF 3-MANIFOLDS
GLUING EQUATIONS equation
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2015/12/17
In [11] we parametrized boundary-unipotent representations of a 3-manifold
group into SL(n; C) using Ptolemy coordinates, which were inspired by A-coordinates on
higher Teichmuller space due to Foc...
On the deformation theory of represen tations of fundamen talgroups of compact hyprbolic 3-manifolds
deformation theory fundamental groups compact hyperbolic 3-manifolds
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2015/10/14
On the deformation theory of represen tations of fundamen talgroups of compact hyprbolic 3-manifolds.
HODGE TYPE THEOREMS FOR ARITHMETIC MANIFOLDS ASSOCIATED TO ORTHOGONAL GROUPS
HODGE TYPE THEOREMS ARITHMETIC MANIFOLDS ORTHOGONAL GROUPS
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2015/10/14
We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds ge...
CONFORMAL ACTIONS OF NILPOTENT GROUPS ON PSEUDO-RIEMANNIAN MANIFOLDS
CONFORMAL ACTIONS PSEUDO-RIEMANNIAN MANIFOLDS
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2015/10/14
We study conformal actions of connected nilpotent Lie groups
on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q)
compact manifold M supports a conformal action of a connected nilpo...
Dynamics on Lorentz manifolds ENSET Oran, November 4-9, 2006
ENSET Oran Dynamics
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2015/10/14
This course was given at ENSET Oran, November 4-9, 2006. It is
an introduction to isometric actions of Lie groups on Lorentz manifolds.
Several examples are presented, followed by general defi...
Isometric actions of Heisenberg groups on compact Lorentz manifolds
Heisenberg groupsl Lorentz manifolds
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2015/10/14
We prove results toward classifying compact Lorentz manifolds on
which Heisenberg groups act isometrically. We give a general construction,
leading to a new example, of codimension-one actions—those...
Compact Lorentz manifolds with local symmetry
local symmetry Lorentz manifolds
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2015/10/14
We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical,
real-analytic, complete Lorentz manifold such that the isometry grou...
FINITE-SIDED DEFORMATION SPACES OF COMPLETE AFFINE 3-MANIFOLDS
3-MANIFOLDS DEFORMATION SPACES
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2015/9/29
A Margulis spacetime is a complete affine 3-manifold
M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S.
We show that eve...
Locally homogeneous geometric manifolds
geometric manifolds collection
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2015/9/29
Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on
topological spaces locally model...
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...
AFFINE MANIFOLDS AND ORBITS OF ALGEBRAIC GROUPS
AFFINE MANIFOLDS ALGEBRAIC GROUPS
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2015/9/29
This paper is the sequel to The radiance obstruction and par-
allel forms on a;ffne manifolds (lYans. Amer. Math. Soc. 286 (1984),
629 649) which introduced a new family of secondary characteristi...