Small intersection numbers in the curve graph

Let $S_{g,p}$ denote the genus $g$ orientable surface with $p \ge 0$ punctures, and let $\omega(g,p)= 3g+p-4$. We prove the existence of infinitely long geodesic rays $\left\{v_{0},v_{1}, v_{2}, ...\right\}$ in the curve graph satisfying the following optimal intersection property: for any natural number $k$, the endpoints $v_{i},v_{i+k}$ of any length $k$ subsegment intersect $O(\omega^{k-2})$ times. By combining this with work of the first author, we answer a question of Dan Margalit.Comment: 13 pages, 6 figure

On the topology of ending lamination space

We show that if S is a finite type orientable surface of genus g and p punctures where 3g+p > 4, then EL(S) is (n-1)-connected and (n-1)-locally connected where dim(PML(S))=2n+1=6g+2p-7. Furthermore, if g=0, then EL(S) is homeomorphic to the p-4 dimensional Nobeling space

Examples of amalgamated free products and coupling rigidity

We present amalgamated free products satisfying coupling rigidity with respect to the automorphism group of the associated Bass-Serre tree. As an application, we obtain orbit equivalence rigidity for amalgamated free products of mapping class groups.Comment: 28 pages, 1 figure. This is an expansion of a part of v1 in arXiv:0902.288

On the Meissner Effect of the Odd-Frequency Superconductivity with Critical Spin Fluctuations: Possibility of Zero Field FFLO pairing

We investigate the influence of critical spin fluctuations on electromagnetic responses in the odd-frequency superconductivity. It is shown that the Meissner kernel of the odd-frequency superconductivity is strongly reduced by the critical spin fluctuation or the massless spin wave mode in the antiferromagnetic phase. These results imply that the superfluid density is reduced, and the London penetration depth is lengthened for the odd-frequency pairing. It is also shown that the zero field Flude-Ferrell-Larkin-Ovchinnikov pairing is spontaneously realized both for even- and odd-frequency in the case of sufficiently strong coupling with low lying spin-modes.Comment: 10 pages, 7 figure

A priori mixed hadrons, hyperon non-leptonic decays, and the |\Delta I|=1/2 rule

The |\Delta I|=1/2 rule in non-leptonic decays of hyperons can be naturally understood by postulating a priori mixed physical hadrons, along with the isospin invariance of the responsible transition operator. It is shown that this operator can be identified with the strong interaction Yukawa hamiltonian.Comment: Workshops on Particles and Fields and Phenomenology of Fundamental Interactions. J. C. D'Olivo, A. Fernandez, and M. A. Perez, Ed

Dimension and rank for mapping class groups

We study the large scale geometry of the mapping class group, MCG. Our main result is that for any asymptotic cone of MCG, the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG. An application is an affirmative solution to Brock-Farb's Rank Conjecture which asserts that MCG has quasi-flats of dimension N if and only if it has a rank N free abelian subgroup. We also compute the maximum dimension of quasi-flats in Teichmuller space with the Weil-Petersson metric.Comment: Incorporates referee's suggestions. To appear in Annals of Mathematic

Stability analysis for parameterized variational systems with implicit constraints

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non-restrictive) qualification conditions. Despite the very general problem setting, the resulting conditions are workable as documented by some academic examplesComment: 26 page