Noncomplex smooth 4-manifolds with Lefschetz fibrations

For every integer g ≥ 2 there exist infinitely many pairwise nonhomeomorphic smooth 4-manifolds admitting genus-g Lefschetz fibration over S2 but not carrying any complex structure. This extends a recent result of Ozbagci and Stipsicz.


Invariant subspaces for Banach space operators with an annular spectral set
Yavuz, Onur (2008-01-01)
Consider an annulus Omega = {z epsilon C : r(0) 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).
Non-commutative holomorphic functions in elements of a Lie algebra and the absolute basis problem
Dosi (Dosiev), A. A. (IOP Publishing, 2009-11-01)
We study the absolute basis problem in algebras of holomorphic functions in non-commuting variables generating a finite-dimensional nilpotent Lie algebra g. This is motivated by J. L. Taylor's programme of non-commutative holomorphic functional calculus in the Lie algebra framework.
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications
Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
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.
Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes
Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01)
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L (1) norm is of order h (1/4) at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theo...
Citation Formats
M. Korkmaz, “Noncomplex smooth 4-manifolds with Lefschetz fibrations,” INTERNATIONAL MATHEMATICS RESEARCH NOTICES, pp. 115–128, 2001, Accessed: 00, 2020. [Online]. Available: