Small Lefschetz fibrations and exotic 4-manifolds

Baykur, R. Inanc
Korkmaz, Mustafa
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 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 CP2#4CP (CP) over bar (2) and 3CP(2)#6CP (CP) over bar (2) from small Lefschetz fibrations over surfaces of higher genera.


Operators commuting with mixing sequences
Ha, MD (Duke University Press; 1999-09-01)
Let (X, F, mu) be a probability space and let L-2(X, 0) be the collection of all f is an element of L-2(X) with zero integrals. A collection A of linear operators on L-2(X) is said to satisfy the Gaussian-distribution property (G.D.P.) if L-2(X, 0) is invariant under A and there exists a constant C < infinity such that the following condition holds:
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.
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.
Imbedding of power series spaces and spaces of analytic functions
Aytuna, A.; Krone, J.; Terzioĝlu, T. (Springer Science and Business Media LLC, 1990-12)
The diametral dimension of a nuclear Fréchet spaceE, which satisfies (DN) and (Ω), is related to power series spaces Λ1(ε) and Λ∞(ε) for some exponent sequence ε. It is proved thatE contains a complemented copy of Λ∞(ε) provided the diametral dimensions ofE and Λ∞(ε) are equal and ε is stable. Assuming Λ1(ε) is nuclear, any subspace of Λ1(ε) which satisfies (DN), can be imbedded intoE. Applications of these results to spaces of analytic functions are given.
On entire rational maps of real surfaces
Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01)
In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
Citation Formats
R. I. Baykur and M. Korkmaz, “Small Lefschetz fibrations and exotic 4-manifolds,” MATHEMATISCHE ANNALEN, pp. 1333–1361, 2017, Accessed: 00, 2020. [Online]. Available: