arXiv subjects

Paolo Aceto

Publications and source records attributed to Paolo Aceto.

21 records · Page 2Linked to original sources

arXiv2016

Dehn surgeries and rational homology balls

We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsváth and Szabó's correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then turn our attention to the case of integral surgeries, with particular emphasis on positive torus knots. Finally, combining these results with a lattice-theoretic obstruction based on Donaldon's theorem, we classify which integral surgeries along torus knots of the form $T_{kq\pm 1,q}$ bound rational homology balls.

math.GT↗

arXiv2015

Rational homology cobordisms of plumbed 3-manifolds

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 $S^1\times S^2$'s bound rational homology $S^1\times D^3$'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 first Betti number equal to 1. By adapting an obstruction based on Donaldson's diagonalization theorem we characterize all manifolds in F that bound rational homology $S^1\times D^3$'s. For all these manifolds a rational homology cobordism to $S^1\times S^2$ 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. In a subsequent paper we describe applications to arborescent link concordance.

math.GT↗

arXiv2015

Symmetric ribbon disks

We study the ribbon discs that arise from a symmetric union presentation of a ribbon knot. A natural notion of symmetric ribbon number is introduced and compared with the classical ribbon number. We show that the gap between these numbers can be arbitrarily large by constructing an infinite family of ribbon knots with ribbon number 2 and arbitrarily large symmetric ribbon number. The proof is based on a particularly simple description of symmetric unions in terms of certain band diagrams which leads to an upper bound for the Heegaard genus of their branched double covers.

math.GT↗