3‐manifolds efficiently bound 4‐manifolds

By Francesco Costantino, Dylan Thurston. 2005

89 citations recorded by the source corpus.

It has been known since 1954 that every 3‐manifold bounds a 4‐manifold. Thus, for instance, every 3‐manifold has a surgery diagram. There are several proofs of this fact, but little attention has been paid to the complexity of the 4‐manifold produced. Given a 3‐manifold M3 of complexity n, we construct a 4‐manifold bounded by M of complexity O(n2), where the ‘complexity’ of a piecewise‐linear manifold is the minimum number of n‐simplices in a triangulation.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e5984353accc678012e1736f5b4dc9114c4291e5

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

6j–symbols, hyperbolic structures and the volume conjecture (2006, background): “Theorem 2.7 (F.C. & D.P. Thurston, [ 6 ]).”
Singularities, Expanders and Topology of Maps. Part 1: Homology Versus Volume in the Spaces of Cycles (2009, background): “The critical set Σ ⊂ Y of the generic map F : X(3) → Y 2 is a curve whose singular points (if any) are double points and cusps and the bound on ||X||∆, due to Costantino-Thurston in a sharper form [10], can be seen as follows.”