Exotic torus manifolds and equivariant smooth structures on quasitoric manifolds

In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties, so-called torus manifolds. For example we show that there are homotopy equivalent torus manifolds which are not homeomorphic. Moreover, we characterize those groups which appear as the fundamental groups of locally standard torus manifolds. In the second part we give a classification of quasitoric manifolds and certain six-dimensional torus manifolds up to equivariant diffeomorphism. In the third part we enumerate the number of conjugacy classes of tori in the diffeomorphism group of torus manifolds. For torus manifolds of dimension greater than six there are always infinitely many conjugacy classes. We give examples which show that this does not hold for six-dimensional torus manifolds.Comment: 21 pages, 2 figures, results about quasitoric manifolds adde

Plaquette operators used in the rigorous study of ground-states of the Periodic Anderson Model in D=2D = 2 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

Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page

Further restrictions on the topology of stationary black holes in five dimensions

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.Comment: LaTex, 22 pages, 9 figure

Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals

Khoo et al.1, 2 have shown that nanosphere dispersed nematic liquid crystal (NDLC) constitutes a new type of metamaterial with index of refraction tunable from negative to positive values. Recently3 we have combined this approach with Monte Carlo simulations of inhomogeneous molecular order in planar NLC cells. Lebwohl - Lasher effective hamiltonian with Rapini - Papoular term for anchoring forces was used. Electric field and amplitude of anchoring forces are control parameters which determine the profiles of order parameter. In this paper we study, using the same approach, local spatial distribution of refractive index in NDLC planar cell. We show that NDLC material consists of layers with negative-zero-positive index of refraction. The spatial organization of those layers strongly depends on incident light wavelength. The role of spatially modulated external electric field for tuning of refractive index of NDLC is briefly discussed

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

Branched Polymers and Hyperplane Arrangements

Original manuscript December 17, 2009We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie (Ann Math, 158:1019–1039, 2003), and Kenyon and Winkler (Am Math Mon, 116(7):612–628, 2009) to any central hyperplane arrangement A A . The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A A is expressed through the value of the characteristic polynomial of A A at 0. We give a more general definition of the space of branched polymers, where we do not require connectivity, and introduce the notion of q-volume for it, which is expressed through the value of the characteristic polynomial of A A at −q − q . Finally, we relate the volume of the space of branched polymers to broken circuits and show that the cohomology ring of the space of branched polymers is isomorphic to the Orlik–Solomon algebra.National Science Foundation (U.S.) (Grant DMS 6923772)National Science Foundation (U.S.) (CAREER Award DMS 0504629

Remarks on the classification of quasitoric manifolds up to equivariant homeomorphism

We give three sufficient criteria for two quasitoric manifolds (M,M') to be (weakly) equivariantly homeomorphic. We apply these criteria to count the weakly equivariant homeomorphism types of quasitoric manifolds with a given cohomology ring.Comment: 11 page

Surgery groups of the fundamental groups of hyperplane arrangement complements

Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular, for the Artin full braid groups. As a consequence we explicitly compute the surgery groups of the Artin pure braid groups. This is obtained as a corollary to a computation of the surgery groups of a more general class of groups, namely for the fundamental group of the complement of any fiber-type hyperplane arrangement in the complex n-space.Comment: 11 pages, AMSLATEX file, revised following referee's comments and suggestions, to appear in Archiv der Mathemati

5-dimensional contact SO(3)-manifolds and Dehn twists

In this paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that all simply connected 5-manifoldswith singular orbits are realized by a Brieskorn manifold with exponents (k,2,2,2). The standard contact structure on such a manifold gives right-handed Dehn twists, and a second contact structure defined in the article gives left-handed twists.Comment: 16 pages, 1 figure; simplification of arguments by restricting classification to coorientation preserving contactomorphism