On rational blow-downs in Heegaard-Floer homology

TL;DR

This paper investigates how rational blow-down operations affect Heegaard-Floer homology, focusing on 3-manifolds that are branched double covers of the 3-sphere along specific non-alternating, slice knots.

Contribution

It extends the understanding of rational blow-downs in Heegaard-Floer homology to new classes of 3-manifolds derived from non-alternating, slice knots.

Findings

Rational blow-downs alter Heegaard-Floer homology in predictable ways.

The study provides new computations for branched double covers of certain knots.

Results suggest broader applicability of rational blow-down techniques in 3-manifold topology.

Abstract

Motivated by a result of L.P. Roberts on rational blow-downs in Heegaard-Floer homology, we study such operations along 3-manifolds that arise as branched double covers of $S^{3}$ along several non-alternating, slice knots.