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Moving closer: contractive maps on discrete metric spaces and graphs
Moving closer discrete metric spaces and graphs
2010/11/23
We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide s...
Let $C^*(E)$ be the graph $C^*$-algebra associated to a graph E and let J be a gauge invariant ideal in $C^*(E)$. We compute the cyclic six-term exact sequence in $K$-theory of the associated extensio...
An analogue of the Harer-Zagier formula for unicellular maps on general surfaces
the Harer-Zagier formula unicellular maps on general surfaces
2010/11/15
A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is simply connected. In a famous article, Harer and Zagier established a formula fo...
Degree growth of monomial maps and McMullen's polytope algebra
monomial maps McMullen's polytope algebra
2010/11/18
We compute all dynamical degrees of monomial maps. Our approach is based on the isomorphism between the polytope algebra of P. McMullen and the universal cohomology of complete toric varieties.
Extremal maps in best constants vector theory - Part I: Duality and Compactness
Extremal maps constants vector theory - Part I
2010/11/11
We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser est...
Symplectic maps to projective spaces and symplectic invariants
Symplectic maps projective spaces symplectic invariants
2010/3/1
After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of \CP2, we describe a new construction of maps from symplectic manifolds of any dimension to \CP2 and the...
Real Gromov-Witten Invariants on the Moduli Space of Genus 0 Stable Maps to a Smooth Rational Projective Space
Gromov-Witten invariant enumerative invariant transversality intersection multiplicity real structure
2010/2/25
We characterize transversality, non-transversality properties on the moduli space of genus 0 stable maps to a rational projective surface. If a target space is equipped with a real structure, i.e, ant...