152 research outputs found
Critical points and resonance of hyperplane arrangements
If F is a master function corresponding to a hyperplane arrangement A and a
collection of weights y, we investigate the relationship between the critical
set of F, the variety defined by the vanishing of the one-form w = d log F, and
the resonance of y. For arrangements satisfying certain conditions, we show
that if y is resonant in dimension p, then the critical set of F has
codimension at most p. These include all free arrangements and all rank 3
arrangements.Comment: revised version, Canadian Journal of Mathematics, to appea
Exact Insulating and Conducting Ground States of a Periodic Anderson Model in Three Dimensions
We present a class of exact ground states of a three-dimensional periodic
Anderson model at 3/4 filling. Hopping and hybridization of d and f electrons
extend over the unit cell of a general Bravais lattice. Employing novel
composite operators combined with 55 matching conditions the Hamiltonian is
cast into positive semidefinite form. A product wave function in position space
allows one to identify stability regions of an insulating and a conducting
ground state. The metallic phase is a non-Fermi liquid with one dispersing and
one flat band.Comment: 4 pages, 3 figure
Seifert fibered contact three-manifolds via surgery
Using contact surgery we define families of contact structures on certain
Seifert fibered three-manifolds. We prove that all these contact structures are
tight using contact Ozsath-Szabo invariants. We use these examples to show
that, given a natural number n, there exists a Seifert fibered three-manifold
carrying at least n pairwise non-isomorphic tight, not fillable contact
structures.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-12.abs.htm
Plaquette operators used in the rigorous study of ground-states of the Periodic Anderson Model in dimensions
The derivation procedure of exact ground-states for the periodic Anderson
model (PAM) in restricted regions of the parameter space and D=2 dimensions
using plaquette operators is presented in detail. Using this procedure, we are
reporting for the first time exact ground-states for PAM in 2D and finite value
of the interaction, whose presence do not require the next to nearest neighbor
extension terms in the Hamiltonian. In order to do this, a completely new type
of plaquette operator is introduced for PAM, based on which a new localized
phase is deduced whose physical properties are analyzed in detail. The obtained
results provide exact theoretical data which can be used for the understanding
of system properties leading to metal-insulator transitions, strongly debated
in recent publications in the frame of PAM. In the described case, the lost of
the localization character is connected to the break-down of the long-range
density-density correlations rather than Kondo physics.Comment: 34 pages, 5 figure
Torsion in Milnor fiber homology
In a recent paper, Dimca and Nemethi pose the problem of finding a
homogeneous polynomial f such that the homology of the complement of the
hypersurface defined by f is torsion-free, but the homology of the Milnor fiber
of f has torsion. We prove that this is indeed possible, and show by
construction that, for each prime p, there is a polynomial with p-torsion in
the homology of the Milnor fiber. The techniques make use of properties of
characteristic varieties of hyperplane arrangements.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-16.abs.htm
Higher homotopy groups of complements of complex hyperplane arrangements
We generalize results of Hattori on the topology of complements of hyperplane
arrangements, from the class of generic arrangements, to the much broader class
of hypersolvable arrangements. We show that the higher homotopy groups of the
complement vanish in a certain combinatorially determined range, and we give an
explicit Z\pi_1-module presentation of \pi_p, the first non-vanishing higher
homotopy group. We also give a combinatorial formula for the \pi_1-coinvariants
of \pi_p.
For affine line arrangements whose cones are hypersolvable, we provide a
minimal resolution of \pi_2, and study some of the properties of this module.
For graphic arrangements associated to graphs with no 3-cycles, we obtain
information on \pi_2, directly from the graph. The \pi_1-coinvariants of \pi_2
may distinguish the homotopy 2-types of arrangement complements with the same
\pi_1, and the same Betti numbers in low degrees.Comment: 24 pages, 3 figure
Homology of iterated semidirect products of free groups
Let be a group which admits the structure of an iterated semidirect
product of finitely generated free groups. We construct a finite, free
resolution of the integers over the group ring of . This resolution is used
to define representations of groups which act compatibly on , generalizing
classical constructions of Magnus, Burau, and Gassner. Our construction also
yields algorithms for computing the homology of the Milnor fiber of a
fiber-type hyperplane arrangement, and more generally, the homology of the
complement of such an arrangement with coefficients in an arbitrary local
system.Comment: 31 pages. AMSTeX v 2.1 preprint styl
Boundary manifolds of projective hypersurfaces
We study the topology of the boundary manifold of a regular neighborhood of a
complex projective hypersurface. We show that, under certain Hodge theoretic
conditions, the cohomology ring of the complement of the hypersurface
functorially determines that of the boundary. When the hypersurface defines a
hyperplane arrangement, the cohomology of the boundary is completely determined
by the combinatorics of the underlying arrangement and the ambient dimension.
We also study the LS category and topological complexity of the boundary
manifold, as well as the resonance varieties of its cohomology ring.Comment: 31 pages; accepted for publication in Advances in Mathematic
Gas-sensitive properties of oxide systems based on ln203 and Sn02 obtained by sol-gel technology
The influence of structural features of ln203, Sn02, Mo03 and Fe203 simple oxides and their composites on the properties of the corresponding semiconductor gas sensors with regards to different gases (CO, CH4, NH3, C2H5OH, CH3OH, NO, N02, 03) have been studied. Structural peculiarities of oxide systems obtained by sol-gel technology have been considered. It was shown the possibility to control the sensor sensitivity to the mentioned above gases by varying chemical composition of sensitive materials and adjusting their structure, as well as by regulat-ing of detecting temperatur
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