## About

24

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Introduction

**Skills and Expertise**

Additional affiliations

November 2019 - present

September 2017 - November 2019

November 2013 - September 2017

Education

December 2007 - December 2008

## Publications

Publications (24)

We give a new elementary proof of the parallelizability of closed orientable 3-manifolds.

We prove that every smooth closed manifold admits a smooth real-valued function with only two critical values. We call a function of this type a Reeb function. We prove that for a Reeb function we can prescribe the set of minima (or maxima), as soon as this set is a PL subcomplex of the manifold. In analogy with Reeb's Sphere Theorem, we use such f...

The ball to ball theorem is presented, which states that a map from the 4-ball to itself, restricting to a homeomorphism on the 3-sphere, whose inverse sets are null and have nowhere dense image, is approximable by homeomorphisms relative to the boundary. The approximating homeomorphisms are produced abstractly, as in the previous chapter, with no...

We prove that any closed simply-connected smooth 4-manifold is 16-fold branched covered by a product of an orientable surface with the 2-torus, where the construction is natural with respect to spin structures. We also discuss analogous results for other families of 4-manifolds with infinite fundamental groups.

We establish the method of holomorphic handle attaching to the strongly pseudoconcave boundary of a complex surface. We use this for proving the following statements: (1) every closed connected oriented contact 3-manifold can be filled as the strongly pseudoconcave boundary of a compact complex surface; (2) any two closed connected oriented contact...

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

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 a...

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...

We provide new branched covering representations for bounded and/or non-compact 4-manifolds, which extend the known ones for closed 4-manifolds.
Assuming M to be a connected oriented PL 4-manifold, our main results are the following: (1) if M is compact with (possibly empty) boundary, there exists a simple branched cover p : M ---> S^4 - Int(B^4_...

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

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 a...

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

In this paper we prove that the closed 4-ball admits non-Kähler complex structures with strictly pseudoconcave boundary. Moreover, the induced contact structure on the boundary 3-sphere is overtwisted.

We give necessary and sufficient conditions for a 4-manifold to be a branched covering of CP^2 and of a sphere bundle over a sphere, which are expressed in terms of the Betti numbers and the intersection form of the 4-manifold. Moreover, we extend these results to include branched coverings of connected sums of the above manifolds.

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.

We prove that any compact almost complex manifold (M, J) of real dimension 2m admits a pseudo-holomorphic embedding in a Euclidean space of dimension 4m + 2 endowed with a suitable non-standard almost complex structure. Moreover, we give a necessary and sufficient condition, expressed in terms of the total Chern class c(M, J), for the existence of...

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

We provide a complete set of moves relating any two Lefschetz fibrations 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.

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...

We show that any compact almost-complex manifold of complex dimension m can be pseudo-holomorphically embedded in R^(6m) equipped with a suitable almost-complex structure.

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 cove...

We construct an orientable ribbon surface F in B^4, which is universal in the following sense: any compact orientable pl 4-manifold having a handle decomposition with 0-, 1- and 2-handles can be represented as a cover of B^4 branched over F.

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.

Closed braided surfaces in S^4 are the two-dimensional analogous of closed braids in S^3. They are useful in studying smooth closed orientable surfaces in S^4, since any such a surface is isotopic to a braided one. We show that the non-orientable version of this result does not hold, that is smooth closed non-orientable surfaces cannot be braided....