The logarithms of Dehn twists on non-orientable surfaces

2014/05/09 by Shunsuke Tsuji, Tsuji, Shunsuke
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.1405.2161

6 pages, 1 figure

arxiv created 2014/05/09 · openalex publication_date 2014/05/09 · arxiv updated 2014/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a Lie algebra associated with a non-orientable surface, which is an analogue for the Goldman Lie algebra of an oriented surface. As an application, we deduce an explicit formula of the Dehn twist along an annulus simple closed curve on the surface as in Kawazumi-Kuno and Masseyeau-Turaev.

Citations

• The Goldman bracket characterizes homeomorphisms

Related

• The logarithms of Dehn twists
• An algebraic characterization of a Dehn twist for nonorientable surfaces
• Roots of Dehn twists
• Dehn twists on Kauffman bracket skein algebras
• The generalized Dehn twist along a figure eight