On modular functors and the ideal Teichmüller tower. (English) Zbl 1149.55015

The purpose of this note is to connect certain results of Hatcher, Lochak and Schneps on the Teichmueller tower of mapping class groups with the language of mathematical conformal field theory introduced by Segal. These results realized a part of Grothendieck’s Esquisse d’un programme. In that formalism, modular functors and conformal field theories are (lax) morphisms of certain structures which they call lax commutative monoids with cancellation. Here the main point is to study these structures along with the morphisms. The authors prove the main theorem which says that the Hatcher-Lochak-Schneps group \(\Lambda\) acts on the profinite completion of \(C_{\text{top}},\) and hence on modular functors with a finiteness condition.


55U40 Topological categories, foundations of homotopy theory
55P65 Homotopy functors in algebraic topology
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