Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

Rational homology cobordisms of plumbed 3-manifolds and arborescent link concordance

Paolo Aceto

created by daniele on 13 Apr 2015

15 apr 2015 -- 14:30

Sala Seminari, DM, Pisa

Seminari di Geometria, Pisa


We investigate rational homology cobordisms of $3$-manifolds with non-zero first Betti number. This is motivated by the natural generalization of the slice-ribbon conjecture to multicomponent links.

In particular we consider the problem of which rational homology $S^1x S^2$'s bound rational homology $S^1xD^3$'s. We give a simple procedure to construct rational homology cobordisms between plumbed 3-manifold. We introduce a family F of plumbed 3-manifolds with b1=1. By adapting an obstruction based on Donaldson's diagonalization theorem we characterize all manifolds in F that bound rational homology $S^1xD^3$'s. For all these manifolds a rational homology cobordism to $S^1xS^2$ can be constructed via our procedure. The family F is large enough to include all Seifert fibered spaces over the $2$-sphere with vanishing Euler invariant.

We also describe applications to arborescent link concordance.

Credits | Cookie policy | HTML 5 | CSS 2.1