Algebraic & Geometric Topology

Pair of pants decomposition of $4$–manifolds

Marco Golla and Bruno Martelli

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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.

Article information

Algebr. Geom. Topol., Volume 17, Number 3 (2017), 1407-1444.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M99: None of the above, but in this section 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]

4-manifolds pair of pants


Golla, Marco; Martelli, Bruno. Pair of pants decomposition of $4$–manifolds. Algebr. Geom. Topol. 17 (2017), no. 3, 1407--1444. doi:10.2140/agt.2017.17.1407.

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