On stable torsion length of a Dehn twist

In this note we prove that the stable torsion length of a Dehn twist is positive. This, in particular, answers a question of T. E. Brendle and B. Farb in the negative. We also give upper bounds for this length.


On the existence of kappa-existentially closed groups
Kegel, Otto H.; Kaya, Burak; Kuzucuoğlu, Mahmut (2018-09-01)
We prove that a κ-existentially closed group of cardinality λ exists whenever κ ≤ λ are uncountable cardinals with λ^{<κ} = λ. In particular, we show that there exists a κ-existentially closed group of cardinalityκ for regular κ with 2^{<κ} = κ. Moreover, we prove that there exists noκ-existentially closed group of cardinality κ for singular κ. Assuming thegeneralized continuum hypothesis, we completely determine the cardinalsκ ≤ λ for which a κ-existentially closed group of cardinality λ exists
Baykur, R. Inanc; Korkmaz, Mustafa; Monden, Naoyuki (2013-11-01)
We investigate the possible self-intersection numbers for sections of surface bundles and Lefschetz fibrations over surfaces. When the fiber genus g and the base genus h are positive, we prove that the adjunction bound 2h-2 is the only universal bound on the self-intersection number of a section of any such genus g bundle and fibration. As a side result, in the mapping class group of a surface with boundary, we calculate the precise value of the commutator lengths of all powers of a Dehn twist about a bound...
Korkmaz, Mustafa (2012-01-01)
We study the ideal triangulation graph T(S) of an oriented punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of S into the simplicial automorphism group of T(S) is an isomorphism. We also show that, the graph T(S) of such a surface S. equipped with its natural simplicial metric is not Gromov hyperbolic. We also show that if the triangulation graph of two oriented punc...
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 ...
A note on the generalized Matsumoto relation
DALYAN, ELİF; Medetogullari, Elif; Pamuk, Mehmetcik (2017-01-01)
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.
Citation Formats
M. Korkmaz, “On stable torsion length of a Dehn twist,” MATHEMATICAL RESEARCH LETTERS, pp. 335–339, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54199.