81 research outputs found
Accidental parabolics and relatively hyperbolic groups
By constructing, in the relative case, objects analoguous to Rips and Sela's
canonical representatives, we prove that the set of images by morphisms without
accidental parabolic, of a finitely presented group in a relatively hyperbolic
group, is finite, up to conjugacy.Comment: Revision, 24 pages, 4 figure
The Symplectic Penrose Kite
The purpose of this article is to view the Penrose kite from the perspective
of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in
Comm. Math. Phys
Convex Polytopes and Quasilattices from the Symplectic Viewpoint
We construct, for each convex polytope, possibly nonrational and nonsimple, a
family of compact spaces that are stratified by quasifolds, i.e. each of these
spaces is a collection of quasifolds glued together in an suitable way. A
quasifold is a space locally modelled on modulo the action of a
discrete, possibly infinite, group. The way strata are glued to each other also
involves the action of an (infinite) discrete group. Each stratified space is
endowed with a symplectic structure and a moment mapping having the property
that its image gives the original polytope back. These spaces may be viewed as
a natural generalization of symplectic toric varieties to the nonrational
setting.Comment: LaTeX, 29 pages. Revised version: TITLE changed, reorganization of
notations and exposition, added remarks and reference
Toric moment mappings and Riemannian structures
Coadjoint orbits for the group SO(6) parametrize Riemannian G-reductions in
six dimensions, and we use this correspondence to interpret symplectic
fibrations between these orbits, and to analyse moment polytopes associated to
the standard Hamiltonian torus action on the coadjoint orbits. The theory is
then applied to describe so-called intrinsic torsion varieties of Riemannian
structures on the Iwasawa manifold.Comment: 25 pages, 14 figures; Geometriae Dedicata 2012, Toric moment mappings
and Riemannian structures, available at
http://www.springerlink.com/content/yn86k22mv18p8ku2
On the spectra of the quantized action-variables of the compactified Ruijsenaars-Schneider system
A simple derivation of the spectra of the action-variables of the quantized
compactified Ruijsenaars-Schneider system is presented. The spectra are
obtained by combining Kahler quantization with the identification of the
classical action-variables as a standard toric moment map on the complex
projective space. The result is consistent with the Schrodinger quantization of
the system worked out previously by van Diejen and Vinet.Comment: Based on talk at the workshop CQIS-2011 (Protvino, Russia, January
2011), 12 page
Geometric and homological finiteness in free abelian covers
We describe some of the connections between the Bieri-Neumann-Strebel-Renz
invariants, the Dwyer-Fried invariants, and the cohomology support loci of a
space X. Under suitable hypotheses, the geometric and homological finiteness
properties of regular, free abelian covers of X can be expressed in terms of
the resonance varieties, extracted from the cohomology ring of X. In general,
though, translated components in the characteristic varieties affect the
answer. We illustrate this theory in the setting of toric complexes, as well as
smooth, complex projective and quasi-projective varieties, with special
emphasis on configuration spaces of Riemann surfaces and complements of
hyperplane arrangements.Comment: 30 pages; to appear in Configuration Spaces: Geometry, Combinatorics
and Topology (Centro De Giorgi, 2010), Edizioni della Normale, Pisa, 201
Existential questions in (relatively) hyperbolic groups {\it and} Finding relative hyperbolic structures
This arXived paper has two independant parts, that are improved and corrected
versions of different parts of a single paper once named "On equations in
relatively hyperbolic groups".
The first part is entitled "Existential questions in (relatively) hyperbolic
groups". We study there the existential theory of torsion free hyperbolic and
relatively hyperbolic groups, in particular those with virtually abelian
parabolic subgroups. We show that the satisfiability of systems of equations
and inequations is decidable in these groups.
In the second part, called "Finding relative hyperbolic structures", we
provide a general algorithm that recognizes the class of groups that are
hyperbolic relative to abelian subgroups.Comment: Two independant parts 23p + 9p, revised. To appear separately in
Israel J. Math, and Bull. London Math. Soc. respectivel
Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes
The degree zero part of the quantum cohomology algebra of a smooth Fano toric
symplectic manifold is determined by the superpotential function, W, of its
moment polytope. In particular, this algebra is semisimple, i.e. splits as a
product of fields, if and only if all the critical points of W are
non-degenerate. In this paper we prove that this non-degeneracy holds for all
smooth Fano toric varieties with facet-symmetric duals to moment polytopes.Comment: 16 pages; corrected version, published in Electron. Res. Announc.
Math. Sc
Moduli spaces of toric manifolds
We construct a distance on the moduli space of symplectic toric manifolds of
dimension four. Then we study some basic topological properties of this space,
in particular, path-connectedness, compactness, and completeness. The
construction of the distance is related to the Duistermaat-Heckman measure and
the Hausdorff metric. While the moduli space, its topology and metric, may be
constructed in any dimension, the tools we use in the proofs are
four-dimensional, and hence so is our main result.Comment: To appear in Geometriae Dedicata, minor changes to previous version,
19 pages, 6 figure
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