A note on the generalized Matsumoto relation

Medetogullari, Elif
Pamuk, Mehmetcik
We give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.


Automorphisms of curve complexes on nonorientable surfaces
Atalan, Ferihe; Korkmaz, Mustafa (2014-01-01)
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.
Equivariant Picard groups of the moduli spaces of some finite Abelian covers of the Riemann sphere
Ozan, Yıldıray (2023-03-01)
In this note, following Kordek's work we will compute the equivariant Picard groups of the moduli spaces of Riemann surfaces with certain finite abelian symmetries.
A Brief Note on the Noncoprime Regular Module Problem
Güloğlu, Ş.; Ercan, Gülin (2021-01-01)
We consider a special configuration in which a finite group A acts by automorphisms on a finite group G and the semidirect product GA acts on the vector space V by linear transformations and discuss the existence of a regular A-module in VA.
On endomorphisms of surface mapping class groups
Korkmaz, Mustafa (Elsevier BV, 2001-05-01)
In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
A note on the Gauss maps of Cayley-free embeddings into spin(7)-manifolds
Ünal, İbrahim (Elsevier BV, 2018-12-01)
We show that a closed, orientable 4-manifold M admits a Cayley-free embedding into flat Spin(7)-manifold R-8 if and only if both the Euler characteristic chi(M) and the signature tau(M) of M vanish.
Citation Formats
E. DALYAN, E. Medetogullari, and M. Pamuk, “A note on the generalized Matsumoto relation,” TURKISH JOURNAL OF MATHEMATICS, pp. 524–536, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35359.