Geodesic
Pair of pants decomposition of 4–manifolds
Golla, Marco1 ; Martelli, Bruno2
1Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden
2Mathematics Department “Tonelli”, Università di Pisa, Largo Pontecorvo 5, I-56127 Pisa, Italy
Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1407-1444
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Using tropical geometry, Mikhalkin has proved that every smooth complex hypersurface in ℂℙn+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 ℂℙn.

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.

DOI : 10.2140/agt.2017.17.1407
Classification : 57M99, 57N13
Keywords: 4-manifolds, pair of pants

Golla, Marco  1   ; Martelli, Bruno  2

1 Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden
2 Mathematics Department “Tonelli”, Università di Pisa, Largo Pontecorvo 5, I-56127 Pisa, Italy 
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Golla, Marco; Martelli, Bruno. Pair of pants decomposition of 4–manifolds. Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1407-1444. doi: 10.2140/agt.2017.17.1407

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