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.
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.
Liftable homeomorphisms of rank two finite abelian branched covers
Atalan, Ferihe; Medetoğulları, Elif; Ozan, Yıldıray (Springer Nature Switzerland AG, 2020)
We investigate branched regular finite abelian A-covers of the 2-sphere, where every homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. In this study, we prove that if A is a finite abelian p-group of rank k and Σ → S2 is a regular A-covering branched over n points such that every homeomorphism f : S2 → S2 lifts to Σ, then n = k+1. We will also give a partial classification of such covers for rank two finite p-groups. In particular, we prove that for a ...
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.