Osaka Journal of Mathematics

The logarithms of Dehn twists on non-orientable surfaces

Shunsuke Tsuji

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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 [4], [5] and Massuyeau--Turaev [7].

Article information

Osaka J. Math., Volume 53, Number 4 (2016), 1125-1132.

First available in Project Euclid: 4 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N05: Topology of $E^2$ , 2-manifolds 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx]


Tsuji, Shunsuke. The logarithms of Dehn twists on non-orientable surfaces. Osaka J. Math. 53 (2016), no. 4, 1125--1132.

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