1,721,032 research outputs found
Filling Volumes and Simplicial Volume of Mapping Tori
Full text linkIn this thesis we introduce two numerical invariants, namely the integral and the real filling volume, defined on orientation-preserving self-homotopy equivalences f of a closed orientable manifold M. These two invariants catch the complexity of the action of the map on the space of (integral or real) singular chains and they are closely related to the (integral or real) simplicial volume of mapping tori. Indeed, if the map f is a homeomorphism of a closed manifold, the real filling volume of f coincides with the simplicial volume of the mapping torus associated to f. On the other hand, the integral filling volume of f constitutes a lower bound for the integral simplicial volume of the associated mapping torus and an upper bound for the stable integral simplicial volume of the same mapping torus.After general considerations on these invariants, we focus on low dimensional cases: we establish when the real and the integral filling volume of an orientation-preserving self-homotopy equivalence of a surface vanish or do not vanish. By employing the neat relation between the real filling volume of f and the simplicial volume of the corresponding mapping torus, we prove that the real filling volume of f is always zero when M is 3-dimensional, while the same does not hold for the integral filling volume.We finally utilize these results to prove that in dimension 3 integral simplicial volume and triangulation complexity are deeply different, where the triangulation complexity of a manifold is the minimal number of simplices required to triangulate it
Length functions on mapping class groups and simplicial volumes of mapping tori
Full text linkLet M be a closed orientable manifold. We introduce two numerical invariants, called filling volumes, on the mapping class group MCG(M) of M, which are defined in terms of filling norms on the space of singular boundaries on M, both with real and with integral coefficients. We show that filling volumes are length functions on MCG(M), we prove that the real filling volume of a mapping class f is equal to the simplicial volume of the corresponding mapping torus E_f, while the integral filling volume of f is not smaller than the stable integral simplicial volume of E_f.
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We discuss several vanishing and non-vanishing results for the filling volumes. As applications, we show that the hyperbolic volume of 3-dimensional mapping tori is not subadditive with respect to their monodromy, and that the real and the integral filling norms on integral boundaries are often non-biLipschitz equivalent
Integral filling volume, complexity, and integral simplicial volume of 3-dimensional mapping tori
Full text linkWe show that the integral filling volume of a Dehn twist f on a closed oriented surface vanishes, i.e., that the integral simplicial volume of the mapping torus with monodromy f
n
grows sublinearly with respect to n. We deduce a complete characterization of mapping classes on surfaces with vanishing integral filling volume and, building on results by Purcell and Lackenby on the complexity of mapping tori, we show that, in dimension three, complexity and integral simplicial volume are not Lipschitz equivalent
Crystal structure of iodoform at 106 K and of the adduct CHI3 center dot 3(C9H7N). Iodoform as a building block of co-crystals
No full textThe structures of CHI3 and of its adduct with quinoline have been
analyzed using X-ray single crystal diffraction at low (106 K, CHI3) and
room temperature (adduct CHI3 center dot 3(C9H7N)). The disorder of the
molecule is removed at low temperature and the non centrosymmetric
structure in P6(3) space group allows a deep examination of the halogen
bondings in the crystal. The iodine atom clearly shows in the both
compounds its electrophilic and nucleophilic behavior. It is noteworthy
that when iodoform forms adducts involving the three iodine atoms with
Lewis bases, it gives raise to non centrosymmetric crystals, and it is a
good candidate for obtaining new materials. (c) 2012 Elsevier B.V. All
rights reserved
Hydrogen Atoms Location in Os-3(mu-H)(CO)(9)(mu(3),eta(2)-C2H) from Accurate X-Ray Data at 100 K
No full textThe structure of the complex Os-3(mu-H)(CO)(9) (mu(3), eta(2)-C2H) has
been determined using X-ray data collected at low temperature (100 K);
all hydrogen atoms have been located. The asymmetric unit is formed by
two molecules joined through hydrogen bonds involving the hydrogen atoms
of C2H moiety and the oxygen atoms of carbonyl groups. The complex
crystallizes in the monoclinic space group P(2)1/c with a = 12.94040(2),
b = 15.4705(2), c = 16.0164(2) angstrom, beta = 106.0860(10)degrees, and
V = 3,080.85(7) angstrom(3), Z = 8. A molecule is formed by a triangular
Os-3 cluster, with metal atoms bearing terminal CO groups. The
acetylenic residual is formally pi-bonded to two Os atoms in a
perpendicular mode and sigma-linked to the third Os atom. A bridging
hydride atom completes the coordination
The effects of P-T changes on intermolecular interactions in crystal structure of iodoform
Full text linkThe structural transition at different pressures of a halogen and
hydrogen bonded molecular structure (iodoform, CHI3) is described. The
pressures analyzed up to sample decomposition are 0.85 GPa (P1RT) and
2.15 GPa (P2RT); also room conditions (PORT) and low temperature (106 K,
POLT) structures have been reported for comparison. The observed
disorder-order phase transition, from P6(3)/m to P6(3) space group, can
be rationalized by the intermolecular interaction analysis. The
shortening of the distances among iodoform planes, observed during the
compression and the temperature decreasing, determines an ordering of
molecular dipoles in a parallel arrangement: this phase transition
causes a shortening of I center dot center dot center dot I halogen
bondings. The BSSE corrected cohesive energies have been calculated for
all structures at DFT/B3LYP level of theory using a periodic boundary
condition code and the Grimme dispersion correction. Hirshfeld surfaces
and electrostatic potential mapped on charge density isosurfaces have
been computed and their features have been analyzed, in order to better
understand the halogen intermolecular interactions that control the
structural modification of iodoform crystal. (C) 2013 Elsevier B.V. All
rights reserved
o-Benzoquinone dioxime
No full textThe title compound, C6H6N2O2, was obtained as a product of an in vitro study of the metabolism of benzofuroxan. The molecule exhibits a amphi configuration of the oxime groups C=N—OH. One oxime group is involved in the formation of a strong intramolecular O—H...N hydrogen bond, while another links molecules into zigzag chains along the c axis via intermolecular O—H...N hydrogen bonds
4-({4-[Bis(2-cyanoethyl)amino]phenyl}diazenyl)benzenesulfonamide
No full textIn the title compound, C18H16N6O2S, which belongs to the family of azo dyes, the dihedral angle between the benzene rings is 26.16 (7)°. In the crystal, molecules are joined by N—H...N and C—H...N hydrogen bonds into double chains parallel to the a axis
3-Phenylsulfanyl-4-phenylsulfonyl-1,2,5-oxadiazole 2-oxide
No full textIn the title compound, C14H10N2O4S2,the furoxan heterocyclic ring and the two S atoms are almost co-planar, with a mean deviation of 0.036 Å. The bond lengths in the pentagonal ring show electron delocalization and the furoxan N—O bond length is quite short [1.211 (3) Å]. The dihedral angles between the central ring and pendant phenyl rings are 78.05 (14) and 84.28 (2)°
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