Exotic 4-manifolds and hyperelliptic lefschetz fibrations

Altunöz, Tülin
In this thesis, we explicitly construct genus-3 Lefschetz fibrations over S2 whose total space is T2 S2#6CP2 using the monodromy of Matsumoto’s genus-2 Lefschetz fibration over S2. We also present exotic minimal symplectic 4-manifolds 3CP2#kCP2 for k = 13; : : : ; 19 by twisted fiber summing of our monodromy or the genus-3 version of generalized Matsumoto’s fibration constructed by Korkmaz or by applying lantern substitutions to these twisted fiber sums. In addition, we generalize our construction of genus-3 Lefschetz fibration to genus-3k Lefschetz fibrations over S2 using the generalized Matsumoto’s genus-2k Lefschetz fibration over S2 constructed by Korkmaz and independently by Cadavid. Using the generalized version of our monodromy, we derive exotic 4-manifolds via Luttinger surgery and twisted fiber sum. Secondly, we prove that the minimal number of singular fibers in a hyperelliptic Lefschetz fibration over a sphere is 2g + 4 for even g 4 , and also, we find a lower bound for odd g 5 when the fibration is holomorphic. In addition, we discuss the number of singular fibers of a hyperelliptic Lefschetz fibration over a sphere which does not carry a complex structure.


Genus-3 Lefschetz Fibrations and Exotic 4-Manifolds with b(2)(+)=3
Altunöz, Tülin (2021-06-01)
We explicitly construct a genus-3 Lefschetz fibration over S-2, whose total space is T-2 x S-2 #6 (CP2) over bar using the monodromy of Matsumoto's genus-2 Lefschetz fibration. We then construct more genus-3 Lefschetz fibrations, whose total spaces are exotic minimal symplectic 4-manifolds 3CP(2)#q (CP2) over bar for q = 13,..., 19. We also generalize our construction to get genus-3k Lefschetz fibration structure on the 4-manifold Sigma(k) x S-2 #6 (CP2) over bar using the generalized Matsumoto's genus-2k L...
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).
Seven, Ahmet İrfan (American Mathematical Society (AMS), 2019-07-01)
In the structure theory of cluster algebras, principal coefficients are parametrized by a family of integer vectors, called c-vectors. Each c-vector with respect to an acyclic initial seed is a real root of the corresponding root system, and the c-vectors associated with any seed defines a symmetrizable quasi-Cartan companion for the corresponding exchange matrix. We establish basic combinatorial properties of these companions. In particular, we show that c-vectors define an admissible cut of edges in the a...
Noncomplex smooth 4-manifolds with Lefschetz fibrations
Korkmaz, Mustafa (2001-01-01)
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).
Citation Formats
T. Altunöz, “Exotic 4-manifolds and hyperelliptic lefschetz fibrations,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.