Canonical extensions of Morita homomorphisms to the Ptolemy groupoid

Details Canonical extensions of Morita homomorphisms to the Ptolemy groupoid Canonical extensions of Morita homomorphisms to the Ptolemy groupoid

2010-06-04

arxiv.org/abs/1006.0920v3

Mathematics

Geometric Topology

30 pages. Minor modifications in this third version

Scientific paper

Let S be a compact connected oriented surface with one boundary component. We extend each of Johnson's and Morita's homomorphisms to the Ptolemy groupoid of S. Our extensions are canonical and take values into finitely generated free abelian groups. The constructions are based on the 3-dimensional interpretation of the Ptolemy groupoid, and a chain map introduced by Suslin and Wodzicki to relate the homology of a nilpotent group to the homology of its Malcev Lie algebra.

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