The Intersection Numbers

Virtual Intersection Numbers

Intersection homology Betti numbers

A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory. The middle-perversity intersection homology with integral coefficients of a compact complex n-dimensional algebraic variety X with isolated singularities is well known to be...

On Kelley’s Intersection Numbers

We introduce a notion of weak intersection number of a collection of sets, modifying the notion of intersection number due to J.L. Kelley, and obtain an analogue of Kelley’s characterization of Boolean algebras which support a finitely additive strictly positive measure. We also consider graph-theoretic reformulations of the notions of intersection number and weak intersection number. Kelley [4...

Subtree and Substar Intersection Numbers

Chang, Y.-W., M.S. Jacobson, CL. Monma and D.B. West, Subtree and substar intersection numbers. Discrete Applied Mathematics 44 (1993) 205-220. We introduce the star number [free number] of a graph, being the minimum t such that G is the intersection graph of unions of t substars [subtrees] of a host tree. We study bounds on these parameters, compare them with interval number, and characterize ...

Word Sequences and Intersection Numbers

There are certain sequences of words in the generators of a twogenerator subgroup of SL(2,C) that frequently arise in the Teichmüller theory of hyperbolic three-manifolds and Kleinian groups. In this paper we establish the connection between two such families, the family of Farey words that have been used by Keen-Series to understand the boundaries of the Quasifuchsian space of surfaces of type...