An infinite family of exotic Dolgachev surfaces without 1- and 3- handles

TL;DR

This paper constructs an infinite family of exotic Dolgachev surfaces that are homeomorphic but not diffeomorphic to the rational surface E(1), all admitting handlebody decompositions without 1- and 3-handles, expanding understanding of smooth structures.

Contribution

It introduces a method to generate infinite exotic Dolgachev surfaces with handlebody decompositions lacking 1- and 3-handles, providing new examples in smooth 4-manifold topology.

Findings

Constructed infinite family of exotic Dolgachev surfaces

Each admits handlebody decomposition without 1- and 3-handles

Provides explicit handlebody diagrams for these surfaces

Abstract

Starting with the Dolgachev surface E(1)_{2,3} we construct an infinite family of distinct exotic copies of the rational surface E(1), each of which admits a handlebody decomposition without 1- and 3- handles, and we draw these handlebodies.