Commutators, Lefschetz fibrations and the signatures of surface bundles

Endo, H
Korkmaz, Mustafa
Kotschick, D
Ozbagci, B
Stipsicz, A
We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with nonzero signature. From these we derive new upper bounds for the minimal genus of a surface representing a given element in the second homology of a mapping class group.


There is no domain representable dense proper subsemigroup of a topological group
Önal, Süleyman (Elsevier BV, 2017-02-01)
We prove that the only domain representable dense subsemigroup of a topological group is itself. Consequently, we obtain that every domain representable subgroup of a topological group is closed.
Equivariant cross sections of complex Stiefel manifolds
Onder, T (Elsevier BV, 2001-01-16)
Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
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.
An obstruction to the existence of real projective structures
Coban, Hatice (Elsevier BV, 2019-09-15)
In this short note, we give an obstruction to obtain examples of higher dimensional manifolds with infinite fundamental groups, including the infinite cyclic group Z, admitting no real projective structure.
Automorphisms of complexes of curves on odd genus nonorientable surfaces
Atalan Ozan, Ferihe; Korkmaz, Mustafa; Department of Mathematics (2005)
Let N be a connected nonorientable surface of genus g with n punctures. Suppose that g is odd and g + n > 6. We prove that the automorphism group of the complex of curves of N is isomorphic to the mapping class group M of N.
Citation Formats
H. Endo, M. Korkmaz, D. Kotschick, B. Ozbagci, and A. Stipsicz, “Commutators, Lefschetz fibrations and the signatures of surface bundles,” TOPOLOGY, pp. 961–977, 2002, Accessed: 00, 2020. [Online]. Available: