Automorphisms of curve complexes on nonorientable surfaces

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2014

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European Mathematical Soc

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g + n >= 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.

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Atalan, Ferihe/0000-0001-6547-0570
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Keywords

Mapping class group, complex of curves, nonorientable surface

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9

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Q3

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Q3

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Volume

8

Issue

1

Start Page

39

End Page

68

URI

https://doi.org/10.4171/GGD/216
 https://hdl.handle.net/20.500.14411/123

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