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Counting Riemann Surfaces

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Counting Surfaces

Part of the book series: Progress in Mathematical Physics ((PMP,volume 70))

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Abstract

In the previous chapter, we have computed the asymptotic generating functions of large maps, and we have seen that they are related to the ( p, q) minimal model.

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Notes

  1. 1.

    Hint: notice that if f is bijective, then exactly one point is sent to \(\infty\), and the fact that f is analytic and bijective means that f can only have one simple pole, and is analytic everywhere else. Then, use that a holomorphic function with no pole on a compact surface can only be a constant.

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Authors and Affiliations

  1. CEA Saclay Institut de Physique Théorique (IPHT), Gif sur Yvette, France

    Bertrand Eynard

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  1. Bertrand Eynard
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Eynard, B. (2016). Counting Riemann Surfaces. In: Counting Surfaces. Progress in Mathematical Physics, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8797-6_6

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