Intersections of curves on surfaces and their applications to mapping class groups

Abstract

We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson homomorphism.

40 pages, 13 figures

References in corpus (5)

• Cohomological Aspects of Magnus Expansions
• Groupoid-theoretical methods in the mapping class groups of surfaces
• 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 (7)

• Groupoid-theoretical methods in the mapping class groups of surfaces
• A regular homotopy version of the Goldman-Turaev Lie bialgebra, the Enomoto-Satoh traces and the divergence cocycle in the Kashiwara-Vergne problem
• Generalized Dehn twists on surfaces and homology cylinders
• A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces
• 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