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BRANCHED SHADOWS AND COMPLEX STRUCTURES ON 4-MANIFOLDS

FRANCESCO COSTANTINO

Institut de Recherche Mathématique Avancée, 7, Rue René Descartes, 67084 Strasbourg Cedex, France

https://doi.org/10.1142/S0218216508006683Cited by:3 (Source: Crossref)

Abstract

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spin^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-dimensional handlebody is homotopic to a complex one.

Keywords:

AMSC: 57M20, 32Q60

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