On closed leaves of foliations, multisections and stable commutator lengths

Details On closed leaves of foliations, multisections and stable commutator lengths On closed leaves of foliations, multisections and stable commutator lengths

2011-05-23

arxiv.org/abs/1105.4444v1

J. Topol. Anal. 4 (2011), no. 3, 491-509

Mathematics

Geometric Topology

16 pages

Scientific paper

We give examples of foliations that answer two questions posed by Mitsumatsu and Vogt about the genus minimising properties of closed leaves of 2-dimensional foliations on 4-manifolds. By studying stable commutator lengths in certain stable mapping class groups, we also answer an asymptotic version of another question of theirs concerning bounds on self-intersection numbers of multisections in surface bundles.

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