Lefschetz Fibrations on 4-manifolds

Date

2009-01-01

Author

Korkmaz, Mustafa

Metadata

Show full item record

Item Usage Stats

101
views

0
downloads

We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces for , and to for . Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spaces are homeomorphic to any other simply-connected 4-manifold with , with one possible exception when . Meanwhile, we produce positive Dehn twist factorizations for several new genus-2 Lefschetz fibrations with small number of critical points, including the smallest possible example, which follow from a reverse engineering procedure we introduce for this setting. We also derive exotic minimal symplectic 4-manifolds in the homeomorphism classes of and from small Lefschetz fibrations over surfaces of higher genera.

URI

https://hdl.handle.net/11511/86333

Relation

Handbook of Teichmuller Theory II

Collections

Department of Mathematics, Book / Book chapter

Suggestions

OpenMETU
Core

Small Lefschetz fibrations and exotic 4-manifolds Baykur, R. Inanc; Korkmaz, Mustafa (Springer Science and Business Media LLC, 2017-04-01) We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces CP2#pCP (CP) over bar (2) for P = 7,8,9, and to 3CP(2)#qCP (CP) over bar (2) for q = 12, . . . , 19. Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spaces are homeomorphic to any other simply-connected 4-manifold with b(+) <= 3, with one possible exception when b(+) = 3. Meanwhile, we produce positive Dehn twist fac...
Kummer extensions of function fields with many rational places Gülmez Temur, Burcu; Özbudak, Ferruh; Department of Mathematics (2005) In this thesis, we give two simple and effective methods for constructing Kummer extensions of algebraic function fields over finite fields with many rational places. Some explicit examples are obtained after a practical search. We also study fibre products of Kummer extensions over a finite field and determine the exact number of rational places. We obtain explicit examples with many rational places by a practical search. We have a record (i.e the lower bound is improved) and a new entry for the table of v...
A generalisation of a theorem of Koldunov with an elementary proof Ercan, Z (Institute of Mathematics, Czech Academy of Sciences, 1999-01-01) We generalize a Theorem of Koldunov [2] and prove that a disjointness preserving quasi-linear operator between Resz spaces has the Hammerstein property.
Lefschetz Fibrations and an Invariant of Finitely Presented Groups Korkmaz, Mustafa (Oxford University Press (OUP), 2009-01-01) Every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. This follows from results of Gompf and Donaldson, and was also proved by Amoros-Bogomolov-Katzarkov-Pantev. We give another proof by providing the monodromy explicitly. We then define the genus of a finitely presented group Gamma to be the minimal genus of a Lefschetz fibration with fundamental group Gamma. We also give some estimates of the genus of certain groups.
Lefschetz fibrations on 4-manifolds Korkmaz, Mustafa (2009-01-01) Lefschetz pencils and fibrations were introduced for studying topological properties of smooth complex projective varieties. More recently, as an application of Donaldson’s asymptotically holomorphic methods [13], Lefschetz pencils have been found on all symplectic manifolds [14], [15]. Conversely, Gompf showed that a 4-manifold admitting a Lefschetz pencil/fibration carries a symplectic structure [23], [24]. Since symplectic 4-manifolds play a prominent role in modern low-dimensional topology, the Donaldso...

Citation Formats

M. Korkmaz, Lefschetz Fibrations on 4-manifolds. 2009, p. 296.