Trisecting 4–manifolds
By David T. Gay, R. Kirby. 2012
177 citations recorded by the source corpus.
We show that any smooth, closed, oriented, connected 4‐manifold can be trisected into three copies of \ k .S 1 B 3 /, intersecting pairwise in 3‐dimensional handlebodies, with triple intersection a closed 2‐dimensional surface. Such a trisection is unique up to a natural stabilization operation. This is analogous to the existence, and uniqueness up to stabilization, of Heegaard splittings of 3‐manifolds. A trisection of a 4‐manifold X arises from a Morse 2‐function GW X! B 2 and the obvious trisection of B 2 , in much the same way that a Heegaard splitting of a 3‐manifold Y arises from a Morse function gW Y ! B 1 and the obvious bisection of B 1 .
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/afbbcea36087c64db0533e9ab8741fe9ca92b05c
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Citations in the corpus
- Diagrams for Relative Trisections (2016, unknown): “Here we rephrase the definition of relative trisection from [Gay and Kirby 2016].”
- Geometric (2019, background): “The primary challenge in classification lies in the prevalence of linearly inseparable problems, where perfectly segregating data points into their respective classes using a linear boundary is infeasible (Minsky & Papert, 1969; Fusi et al., 2016).”