SHADOWS OF 4-MANIFOLDS WITH COMPLEXITY ZERO AND POLYHEDRAL COLLAPSING.

Autor: HIRONOBU NAOE
Předmět:
Zdroj: Proceedings of the American Mathematical Society; Oct2017, Vol. 145 Issue 10, p4561-4572, 12p
Abstrakt: Our purpose is to classify acyclic 4-manifolds having shadow complexity zero. In this paper, we focus on simple polyhedra and discuss this problem combinatorially. We consider a shadowed polyhedron X and a simple polyhedron X0 that is obtained by collapsing from X. Then we prove that there exists a canonical way to equip internal regions of X0 with gleams so that two 4-manifolds reconstructed from X0 and X are diffeomorphic. We also show that any acyclic simple polyhedron whose singular set is a union of circles can collapse onto a disk. As a consequence of these results, we prove that any acyclic 4-manifold having shadow complexity zero with boundary is diffeomorphic to a 4-ball. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index