Canonical extensions of Morita homomorphisms to the Ptolemy groupoid

Gwenael Massuyeau

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arXiv · 1006.0920

Canonical extensions of Morita homomorphisms to the Ptolemy groupoid

Gwenael Massuyeau

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Abstract

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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BibTeX RIS

Gwenael Massuyeau. 2011-06-27. Canonical extensions of Morita homomorphisms to the Ptolemy groupoid. https://arxiv.org/abs/1006.0920

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