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Jérémie Bettinelli

École polytechnique
Laboratoire d'informatique (LIX)
91128 Palaiseau Cedex
FRANCE
E-mail: firstname « . » lastname « at » normalesup « . » org
Office: 2023
Phone: (+33) (0)1 77 57 80 61
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Positive genus with holes

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Finally, we may also consider general orientable surfaces with a boundary, that is, connected sums of tori with disks removed. To give an image of such a thing, recall the gluing of bike tubes from last section and remove a certain number of nonintersecting disks from it. These are the objects studied in Geodesics in Brownian surfaces (Brownian maps).

Torus 10k_60_80 [jpg1jpg2jpg3jpg43D pdfu3d&tex]   Torus 30k_100_120 [jpg1jpg23D pdfu3d&tex]

Genus 1 with 2 holes
Double torus 30k_100_80 [jpg1jpg2jpg3jpg43D pdfu3d&tex]   Triple torus 20k_100_80 [jpg1jpg23D pdfu3d&tex]

Genus 2 and 3 with 2 holes

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