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2017 Pair of pants decomposition of $4$–manifolds
Marco Golla, Bruno Martelli
Algebr. Geom. Topol. 17(3): 1407-1444 (2017). DOI: 10.2140/agt.2017.17.1407

Abstract

Using tropical geometry, Mikhalkin has proved that every smooth complex hypersurface in n+1 decomposes into pairs of pants: a pair of pants is a real compact 2n–manifold with cornered boundary obtained by removing an open regular neighborhood of n + 2 generic complex hyperplanes from n.

As is well-known, every compact surface of genus g 2 decomposes into pairs of pants, and it is now natural to investigate this construction in dimension 4. Which smooth closed 4–manifolds decompose into pairs of pants? We address this problem here and construct many examples: we prove in particular that every finitely presented group is the fundamental group of a 4–manifold that decomposes into pairs of pants.

Citation

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Marco Golla. Bruno Martelli. "Pair of pants decomposition of $4$–manifolds." Algebr. Geom. Topol. 17 (3) 1407 - 1444, 2017. https://doi.org/10.2140/agt.2017.17.1407

Information

Received: 30 June 2015; Revised: 18 May 2016; Accepted: 11 July 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1376.57020
MathSciNet: MR3677932
Digital Object Identifier: 10.2140/agt.2017.17.1407

Subjects:
Primary: 57M99, 57N13

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 3 • 2017
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