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arXiv · hep-th/9701038

Topological charges and the genus of surfaces

Luis J. Boya·Antonio J. Segui-Santonja
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Abstract

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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Luis J. Boya, Antonio J. Segui-Santonja. 1997-01-10. Topological charges and the genus of surfaces. https://doi.org/10.1016/s0393-0440(96)00048-4

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