Mazur manifolds and corks with small shadow complexities

TL;DR

This paper constructs infinitely many Mazur type manifolds and corks with minimal shadow complexity using Turaev's shadow theory, including manifolds from Bing's house, enriching the understanding of 4-manifold topology.

Contribution

It introduces new examples of Mazur type manifolds and corks with shadow complexity one, expanding the class of known 4-manifolds with minimal shadow complexity.

Findings

Existence of infinitely many Mazur type manifolds with shadow complexity one.

Construction of such manifolds from contractible special polyhedra with one true vertex.

Identification of these manifolds within those constructed from Bing's house.

Abstract

In this paper we find infinitely many Mazur type manifolds and corks with shadow complexity one among the 4-manifolds constructed from contractible special polyhedra having one true vertex by using the notion of Turaev's shadow. We also find such manifolds among 4-manifolds constructed from Bing's house. Our manifolds with shadow complexity one contain the Mazur manifolds $W^{\pm }(l,k)$ which were studied by Akbulut and Kirby.