Topological charges and the genus of surfaces

Details Topological charges and the genus of surfaces Topological charges and the genus of surfaces

1997-01-10

arxiv.org/abs/hep-th/9701038v1

J.Geom.Phys. 23 (1997) 76-82

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, Latex. To be published in Journal of Geommetry and Physics

Scientific paper

10.1016/S0393-0440(96)00048-4

We show that the topological charge of the n-soliton solution of the sine-Gordon equation n is related to the genus g > 1 of a constant negative curvature compact surface described by this configuration. The relation is n=2(g-1), where n is even. The moduli space of complex dimension B(g)=3(g-1) corresponds precisely to the freedom to choosing the configuration with n solitons of arbitrary positions and velocities. We speculate also that the odd soliton states will describe the unoriented surfaces.

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