Branched shadows and complex structures of 4-manifolds

Abstract

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with $Spi{n}^c$-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-handlebody is homotopic to a complex one.

24 pages, 9 figures

References in corpus (1)

• A short introduction to shadows of 4-manifolds