Abstract
In this paper we show that there exist 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.
Citation
Hironobu Naoe. "Mazur manifolds and corks with small shadow complexities." Osaka J. Math. 55 (3) 479 - 498, July 2018.