Daniele Zuddas | Università degli Studi di Trieste (original) (raw)

Papers by Daniele Zuddas

Mathematical Research Letters

We prove that compact topological 4-manifolds can be effectively presented by a finite amount of ... more We prove that compact topological 4-manifolds can be effectively presented by a finite amount of data.

$Research paper thumbnail of Non-Kähler complex structures on <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mn>4</mn></msup></mrow><annotation encoding="application/x-tex">\mathbb{R}^4</annotation></semantics></math>R4, II$

Journal of Symplectic Geometry

Geometry & Topology

We construct the first examples of non-Kähler complex structures on R 4 . These complex surfaces ... more We construct the first examples of non-Kähler complex structures on R 4 . These complex surfaces have some analogies with the complex structures constructed in the early fifties by Calabi and Eckmann on the products of two odd-dimensional spheres. However, our construction is quite different from that of Calabi and Eckmann.

$Research paper thumbnail of Non-K "ahler complex structures on $ mathbb{R}^4$$

$Research paper thumbnail of Non-K\" ahler complex structures on <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext> </mtext><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>b</mi><mi>b</mi><msup><mi>R</mi><mn>4</mn></msup></mrow><annotation encoding="application/x-tex">\ mathbb {R}^ 4</annotation></semantics></math> mathbbR4$

We provide a complete set of moves relating any two Lefschetz fibration over the disk having as t... more We provide a complete set of moves relating any two Lefschetz fibration over the disk having as their total space the same 4-dimensional 2-handlebody up to 2-equivalence. As a consequence, we also obtain moves relating diffeomorphic 3-dimensional open books, providing a different approach to an analogous previous result by Harer.

Journal of Knot Theory and Its Ramifications, 2018

We provide a complete set of two moves that suffice to relate any two open book decompositions of... more We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivalent) forms. Our approach relies on 4-dimensional Lefschetz fibrations, and on 3-dimensional contact topology, via the Giroux-Goodman stable equivalence theorem for open book decompositions representing homologous contact structures.

Journal of the London Mathematical Society, 2019

We prove some existence results for branched coverings on 4-manifolds and on 4-dimensional cobord... more We prove some existence results for branched coverings on 4-manifolds and on 4-dimensional cobordisms.

Mathematical Research Letters, 2019

Journal of Symplectic Geometry, 2018

We follow our study of non-Kähler complex structures on R^4 that we defined in our previous paper... more We follow our study of non-Kähler complex structures on R^4 that we defined in our previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their meromorphic functions. We also prove that the Picard groups of these complex surfaces are uncountable, and give an explicit description of the canonical bundle. Finally, we show that any connected non-compact oriented 4-manifold admits complex structures without Kähler metrics.

Topology and its Applications, 2017

Inspired by the analogous result in the algebraic setting (Theorem 1) we show (Theorem 2) that th... more Inspired by the analogous result in the algebraic setting (Theorem 1) we show (Theorem 2) that the product M × RP^n of a closed and orientable topological manifold M with the n-dimensional real projective space cannot be embedded into RP^(m+n+1) for all even n > m.

Journal of Geometry and Physics, 2016

We prove that any compact almost complex manifold (M^(2m), J) of real dimension 2m admits a pseud... more We prove that any compact almost complex manifold (M^(2m), J) of real dimension 2m admits a pseudo-holomorphic embedding in (R^(4m+2), J') for a suitable positive almost complex structure J'. Moreover, we give a necessary and sucient condition, expressed in terms of the Segre class s_m(M, J), for the existence of an embedding or an immersion in (R^(4m), J'). We also discuss the pseudo-holomorphic embeddings of an almost complex 4-manifold in (R^6, J').

Geometry & Topology Monographs, 2015

We construct universal Lefschetz fibrations, defined in analogy with classical universal bundles.... more We construct universal Lefschetz fibrations, defined in analogy with classical universal bundles. We also introduce the cobordism groups of Lefschetz fibrations, and we see how these groups are quotients of the singular bordism groups via the universal Lefschetz fibrations.

Rivista di Matematica della Università di Parma, 2001

In this paper we study the set of self-Bergmann metrics on the Riemann sphere endowed with the Fu... more In this paper we study the set of self-Bergmann metrics on the Riemann sphere endowed with the Fubini-Study metric and we extend a theorem of Tian to the case of the punctured plane endowed with a natural flat metric.

Geometry & Topology, 2017

We construct the first examples of non-Kähler complex structures on R^4. These complex surfaces h... more We construct the first examples of non-Kähler complex structures on R^4. These complex surfaces have some analogies with the complex structures constructed in early Fifties by Calabi and Eckmann on the products of two odd-dimensional spheres. However, our construction is quite different from that of Calabi and Eckmann.

$Research paper thumbnail of A universal ribbon surface in <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>B</mi><mn>4</mn></msup></mrow><annotation encoding="application/x-tex">B^{4}</annotation></semantics></math>B4$

Proceedings of the London Mathematical Society, 2005

We construct an orientable ribbon surface F ⊂ B 4 , which is universal in the following sense: an... more We construct an orientable ribbon surface F ⊂ B 4 , which is universal in the following sense: any orientable 4-manifold M ∼ = B 4 ∪ 1-handles ∪ 2-handles can be represented as a cover of B 4 branched over F .

International Mathematics Research Notices, 2009

We show that any homologically non-trivial Dehn twist of a compact surface F with boundary is the... more We show that any homologically non-trivial Dehn twist of a compact surface F with boundary is the lifting of a half-twist in the braid group B_n, with respect to a suitable branched covering p : F ---> B^2. In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on B^2 is a branched covering of B^2 x B^2.

Algebraic & Geometric Topology, 2012

In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fib... more In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz fibrations when the fiber is the torus or an orientable surface with connected boundary and the base surface is the disk. As a by-product we also get some immersion results for 4-dimensional 2-handlebodies.