Chimneys, leopard spots, and the identities of Basmajian and Bridgeman

We give a simple geometric argument to derive in a common manner orthospectrum identities of Basmajian and Bridgeman. Our method also considerably simplifies the determination of the summands in these identities. For example, for every odd integer n, there is a rational function q_n of degree 2(n-2) so that if M is a compact hyperbolic manifold of dimension n with totally geodesic boundary S, there is an identity \chi(S) = \sum_i q_n(e^{l_i}) where the sum is taken over the orthospectrum of M. When n=3, this has the explicit form \sum_i 1/(e^{2l_i}-1) = -\chi(S)/4.Comment: 6 pages; version 2 incorporates referee's comment

Compressibility of a two-dimensional extended Hubbard model

The compressibility of an extended $d-p$ Hubbard model is investigated by the Roth's two-pole approximation. Using the factorization procedure proposed by Beenen and Edwards, superconductivity with singlet $d_{x^2-y^2}$-wave pairing is also considered. Within this framework, the effects of $d-p$ hybridization and Coulomb interaction $U$ on the compressibility are studied carefully. It has been found that the compressibility diverges and then it becomes negative near the half-filling. Within Roth's method, it has been verified that an important contribution for the negative compressibility comes from the spin-correlation term $$ present in Roth's band shift. This correlation function plays an important role due to its high doping dependence. Also, its effects in the band shift and consequently in the compressibility are pronounced near the half-filling. The numerical results show that the hybridization acts in the sense of suppressing the negative compressibility near half-filling. Finally, the possibility of a connection between the negative compressibility and the phase separation is also discussed.Comment: 3 pages, 1 figure, accepted for publication in Physica

Circular groups, planar groups, and the Euler class

We study groups of C^1 orientation-preserving homeomorphisms of the plane, and pursue analogies between such groups and circularly-orderable groups. We show that every such group with a bounded orbit is circularly-orderable, and show that certain generalized braid groups are circularly-orderable. We also show that the Euler class of C^infty diffeomorphisms of the plane is an unbounded class, and that any closed surface group of genus >1 admits a C^infty action with arbitrary Euler class. On the other hand, we show that Z oplus Z actions satisfy a homological rigidity property: every orientation-preserving C^1 action of Z oplus Z on the plane has trivial Euler class. This gives the complete homological classification of surface group actions on R^2 in every degree of smoothness.Comment: Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper15.abs.htm

Coxeter groups and random groups

For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any density less than a half (or in the few relators model) contains quasiconvex subgroups commensurable with some member of the family, with overwhelming probability.Comment: 18 pages, 14 figures; version 2 incorporates referee's correction

Quasimorphisms and laws

Stable commutator length vanishes in any group that obeys a law

Role of Hybridization in the Superconducting Properties of an Extended d−pd-p Hubbard Model: a Detailed Numerical Study

The Roth's two-pole approximation has been used by the present authors to study the effects of the hybridization in the superconducting properties of a strongly correlated electron system. The model used is the extended Hubbard model which includes the $d-p$ hybridization, the $p$-band and a narrow $d$-band. The present work is an extension a previous reference [Intern. Journ. of Modern Phys. B, Vol. 18 No. 2 (2004) 241]. Nevertheless, some important correlation functions necessary to estimate the Roth's band shift, are included together with the temperature $T$ and the Coulomb interaction $U$ to describe the superconductivity. The superconducting order parameter of a cuprate system, is obtained following Beenen and Edwards formalism. Here, we investigate in detail the change of the order parameter associated to temperature, Coulomb interaction and Roth's band shift effects on superconductivity. The phase diagram with $T_c$ versus the total occupation numbers $n_T$, shows the difference respect to the previous work.Comment: 4 pages, 1 figure, accept to be published in Physica

Real places and torus bundles

If M is a hyperbolic once-punctured torus bundle over the circle, then the trace field of M has no real places.Comment: 15 pages; v4 incorporates referee's comment