Lefschetz Fibrations and an Invariant of Finitely Presented Groups

Download

index.pdf

Date

2009-01-01

Author

Korkmaz, Mustafa

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

152
views

89
downloads

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.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/36975

Journal

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

DOI

https://doi.org/10.1093/imrn/rnn164

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

On a Fitting length conjecture without the coprimeness condition Ercan, Gülin (Springer Science and Business Media LLC, 2012-08-01) Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.
Chirality of real non-singular cubic fourfolds and their pure deformation classification Finashin, Sergey (Springer Science and Business Media LLC, 2020-02-22) In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces can not be continuously deformed to their mirror reflection.
Involutions in locally finite groups Kuzucuoğlu, Mahmut (Wiley, 2004-04-01) The paper deals with locally finite groups G having an involution phi such that C-G(phi) is of finite rank. The following theorem gives a very detailed description of such groups.
Betti numbers of fixed point sets and multiplicities of indecomposable summands Öztürk, Semra (Cambridge University Press (CUP), 2003-04-01) Let G be a finite group of even order, k be a field of characteristic 2, and M be a finitely generated kG-module. If M is realized by a compact G-Moore space X, then the Betti numbers of the fixed point set X-Cn and the multiplicities of indecomposable summands of M considered as a kC(n)-module are related via a localization theorem in equivariant cohomology, where C-n is a cyclic subgroup of G of order n. Explicit formulas are given for n = 2 and n = 4.
A classification of equivariant principal bundles over nonsingular toric varieties Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2016-12-01) We classify holomorphic as well as algebraic torus equivariant principal G-bundles over a nonsingular toric variety X, where G is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.

Citation Formats

M. Korkmaz, “Lefschetz Fibrations and an Invariant of Finitely Presented Groups,” INTERNATIONAL MATHEMATICS RESEARCH NOTICES, pp. 1547–1572, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36975.