The research article “Finite rigid sets in curve complexes of nonorientable surfaces”, co-authored by METU member Prof. Mustafa Korkmaz, has been published in Geometriae Dedicata.
A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite rigid sets in the curve complexes of connected nonorientable surfaces of genus g with n holes for g+ n≠ 4.
Ilbira, S., & Korkmaz, M. (2020). Finite rigid sets in curve complexes of nonorientable surfaces. Geometriae Dedicata, 206(1), 83-103. doi:10.1007/s10711-019-00478-6
Article access: https://link.springer.com/article/10.1007/s10711-019-00478-6
Prof. Mustafa Korkmaz
|About the author||ORCID: 36059157800|
Curve complex, Finite rigid set, Mapping class group, Nonorientable surface
The main result of this paper was part of the first author’s Ph.D. thesis at Middle East Technical University. We learned at the ICM 2018 satellite conference ‘Braid Groups, Configuration Spaces and Homotopy Theory’ held in Salvador, Brazil, that Blazej Szepietowski has independently obtained similar results. The authors would like to thank Szepietowski for pointing out a mistake in the earlier version. The first author would like to thank Mehmetcik Pamuk for helpful conversations. The second author thanks UMass-Amherst Department of Mathematics and Statistics for its hospitality, where the writing of this paper is completed. We are also grateful to the referee for reading the paper carefully and for making many useful suggestions.