Groupoid-theoretical methods in the mapping class groups of surfaces

Abstract

We provide some language for algebraic study of the mapping class groups for surfaces with non-connected boundary. As applications, we generalize our previous results on Dehn twists to any compact connected oriented surfaces with non-empty boundary. Moreover we embed the `smallest' Torelli group in the sense of Putman into a pro-nilpotent group coming from the Goldman Lie algebra. The graded quotients of the embedding equal the Johnson homomorphisms of all degrees if the boundary is connected.

43 pages, 7 figures

References in corpus (5)

• Cohomological Aspects of Magnus Expansions
• Intersections of curves on surfaces and their applications to mapping class groups
• The logarithms of Dehn twists
• New series in the Johnson cokernels of the mapping class groups of surfaces
• The generalized Dehn twist along a figure eight

Cited by in corpus (9)

• Intersections of curves on surfaces and their applications to mapping class groups
• A regular homotopy version of the Goldman-Turaev Lie bialgebra, the Enomoto-Satoh traces and the divergence cocycle in the Kashiwara-Vergne problem
• The quotient of a Kauffman bracket skein algebra by the square of an augmentation ideal
• The Torelli group and the Kauffman bracket skein module
• Poisson algebras of curves on bordered surfaces and skein quantization
• Hodge theory of the Goldman bracket
• Generalized Kronecker formula for Bernoulli numbers and self-intersections of curves on a surface
• Surface topology and involutive bimodules
• The total Johnson homomorphism on the homology cylinder and the bracket-quantization HOMFLY-PT skein algebra