Genus-two trisections are standard
| Autor: | Jeffrey Meier, Alexander Zupan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Heegaard splittings 010102 general mathematics Geometric Topology (math.GT) 02 engineering and technology 01 natural sciences Mathematics::Geometric Topology trisections Combinatorics Mathematics - Geometric Topology Dehn surgery 020901 industrial engineering & automation Corollary Genus (mathematics) 57R65 57M25 FOS: Mathematics 57N12 waves Geometry and Topology Diffeomorphism 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Geom. Topol. 21, no. 3 (2017), 1583-1630 |
| Popis: | We show that the only closed 4-manifolds admitting genus two trisections are $S^2 \times S^2$ and connected sums of $S^1 \times S^3$, $\mathbb{CP}^2$, and $\overline{\mathbb{CP}}^2$ with two summands. Moreover, each of these manifolds admits a unique genus two trisection up to diffeomorphism. The proof relies heavily on the combinatorics of genus two Heegaard diagrams of $S^3$. As a corollary, we classify two-component links contained in a genus two Heegaard surface for $S^3$ with a surface-sloped cosmetic Dehn surgery. Comment: 41 pages, 29 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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