Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 17, Number 3 (2017), 1407-1444.
Pair of pants decomposition of $4$–manifolds
Using tropical geometry, Mikhalkin has proved that every smooth complex hypersurface in decomposes into pairs of pants: a pair of pants is a real compact –manifold with cornered boundary obtained by removing an open regular neighborhood of generic complex hyperplanes from .
As is well-known, every compact surface of genus decomposes into pairs of pants, and it is now natural to investigate this construction in dimension . Which smooth closed –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 –manifold that decomposes into pairs of pants.
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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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. https://projecteuclid.org/euclid.agt/1510841402