1,383 research outputs found
Discrete automorphism groups of convex cones of finite type
We investigate subgroups of SL (n,Z) which preserve an open nondegenerate
convex cone in real n-space and admit in that cone as fundamental domain a
polyhedral cone of which some faces are allowed to lie on the boundary.
Examples are arithmetic groups acting on selfdual cones, Weyl groups of certain
Kac-Moody algebras and do occur in algebraic geometry as the automorphism
groups of projective manifolds acting on their ample cones.Comment: 30 pages, to appear in Compositio Mat
The efficiency of plankton in the utilization of the sun radiation [Translation from: Briroda, 12, 29-35, 1948]
The efficiency of utilisation of the sun's radiation by natural communities has not been properly demonstrated with what so far has been obtained of reliable values, and it represents a great interest in many respects. A systematic study of the biotic balance of lakes was done in the course of a succession of summers starting in 1932, extensive material was obtained, which permitted to compute a value fear the utilisation of the sun's radiation by plankton in lakes, and to compare this with corresponding values for marine plankton and terrestrial vegetation
On the nature of the Virasoro algebra
The multiplication in the Virasoro algebra comes from the commutator in a quasiassociative algebra with the multiplication
\renewcommand{\theequation}{} \be \ba{l} \ds e_p * e_q = - {q (1 + \epsilon
q) \over 1 + \epsilon (p + q)} e_{p+q} + {1 \over 2} \theta \left[p^3 - p +
\left(\epsilon - \epsilon^{-1} \right) p^2 \right] \delta^0_{p+q},
\vspace{3mm}\\ \ds e_p * \theta = \theta* e_p = 0. \ea \ee The multiplication
in a quasiassociative algebra satisfies the property
\renewcommand{\theequation}{} \be a * (b * c) - (a * b) * c = b * (a * c) -
(b * a) * c, \qquad a, b, c \in {\cal R}. \ee This property is necessary and
sufficient for the Lie algebra {\it Lie} to have a phase space. The
above formulae are put into a cohomological framework, with the relevant
complex being different from the Hochschild one even when the relevant
quasiassociative algebra becomes associative. Formula above
also has a differential-variational counterpart
Infinitely many hyperbolic Coxeter groups through dimension 19
We prove the following: there are infinitely many finite-covolume (resp.
cocompact) Coxeter groups acting on hyperbolic space H^n for every n < 20
(resp. n < 7). When n=7 or 8, they may be taken to be nonarithmetic.
Furthermore, for 1 < n < 20, with the possible exceptions n=16 and 17, the
number of essentially distinct Coxeter groups in H^n with noncompact
fundamental domain of volume less than or equal to V grows at least
exponentially with respect to V. The same result holds for cocompact groups for
n < 7. The technique is a doubling trick and variations on it; getting the most
out of the method requires some work with the Leech lattice.Comment: This is the version published by Geometry & Topology on 11 July 2006
(V2: typesetting correction
Rolling of Coxeter polyhedra along mirrors
The topic of the paper are developments of -dimensional Coxeter polyhedra.
We show that the surface of such polyhedron admits a canonical cutting such
that each piece can be covered by a Coxeter -dimensional domain.Comment: 20pages, 15 figure
All flat manifolds are cusps of hyperbolic orbifolds
We show that all closed flat n-manifolds are diffeomorphic to a cusp
cross-section in a finite volume hyperbolic (n+1)-orbifold.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-13.abs.htm
Universal Realisators for Homology Classes
We study oriented closed manifolds M^n possessing the following Universal
Realisation of Cycles (URC) Property: For each topological space X and each
integral homology class z of it, there exist a finite-sheeted covering \hM^n of
M^n and a continuous mapping f of \hM^n to X such that f takes the fundamental
class [\hM^n] to kz for a non-zero integer k. We find wide class of examples of
such manifolds M^n among so-called small covers of simple polytopes. In
particular, we find 4-dimensional hyperbolic manifolds possessing the URC
property. As a consequence, we prove that for each 4-dimensional oriented
closed manifold N^4, there exists a mapping of non-zero degree of a hyperbolic
manifold M^4 to N^4. This was conjectured by Kotschick and Loeh.Comment: 20 pages, 1 figure; in version 2 minor corrections are made, 4
bibliography items and 1 figure are adde
Noncoherence of some lattices in Isom(Hn)
We prove noncoherence of certain families of lattices in the isometry group
of the hyperbolic n-space for n greater than 3. For instance, every nonuniform
arithmetic lattice in SO(n,1) is noncoherent, provided that n is at least 6.Comment: This is the version published by Geometry & Topology Monographs on 29
April 2008. V3: typographical correction
Complete families of commuting functions for coisotropic Hamiltonian actions
Let G be an algebraic group over a field F of characteristic zero, with Lie
algebra g=Lie(G). The dual space g^* equipped with the Kirillov bracket is a
Poisson variety and each irreducible G-invariant subvariety X\subset g^*
carries the induced Poisson structure. We prove that there is a family of
algebraically independent polynomial functions {f_1,...f_l} on X, which
pairwise commute with respect to the Poisson bracket and such that l=(dim
X+tr.deg F(X)^G)/2. We also discuss several applications of this result to
complete integrability of Hamiltonian systems on symplectic Hamiltonian
G-varieties of corank zero and 2.Comment: Changed presentatio
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