Osaka Journal of Mathematics

The logarithms of Dehn twists on non-orientable surfaces

Shunsuke Tsuji

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

Article information

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

Dates
First available in Project Euclid: 4 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1475601835

Mathematical Reviews number (MathSciNet)
MR3554860

Zentralblatt MATH identifier
1361.57028

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

Citation

Tsuji, Shunsuke. The logarithms of Dehn twists on non-orientable surfaces. Osaka J. Math. 53 (2016), no. 4, 1125--1132. https://projecteuclid.org/euclid.ojm/1475601835


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References

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  • V.G. Turaev: Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. (4) 24 (1991), 635–704. \endthebibliography*