1,720,971 research outputs found
Braiding non-orientable surfaces in S^4
No full textClosed braided surfaces in are the two-dimensional analogous of closed braids in . They are usefull in studying smooth closed orientable surfaces in , 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. In fact, any reasonable definition of non-orientable braided surfaces leads to very strong restrictions in terms of self-intersection and Euler characteristic
Some remarks on Bergmann metrics
No full textIn 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
Branched coverings of CP^2 and other basic 4-manifolds
Full text linkWe give necessary and sufficient conditions for a 4-manifold to be a branched covering of CP2, S2xS2, S2x similar to S2 or S3xS1, which are expressed in terms of the Betti numbers and the signature of the 4-manifold. Moreover, we extend these results to include branched coverings of connected sums of the above manifolds. This leads to some new examples of closed simply connected quasiregularly elliptic 4-manifolds
Branched coverings and 4-manifolds, PhD thesis
No full textWe prove that there exists a universal surface in B^4, analogous to universal knots and links in S^3.
We prove that every Dehn twist in a compact orientable surface with boundary is the lift of a half-twist in the disk, with respect to a certain simple branched ccovering
Certifying a compact topological 4-manifold
Full text linkWe prove that compact topological 4-manifolds can be effectively presented by a finite amount of data
On the strongly pseudoconcave boundary of a compact complex surface
No full textIn this paper, 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 non-empty closed connected oriented contact 3-manifolds are complex cobordant. Moreover, we show that such a complex surface (or complex cobordism) can be taken Kahler
A concave holomorphic filling of an overtwisted contact 3-sphere
Full text linkWe prove that the closed 4-ball admits non-Kahler complex structures with strongly pseudoconcave boundary. Moreover, the induced contact structure on the boundary 3-sphere is overtwisted
Representing Dehn twists with branched coverings
No full textWe show that any homologically non-trivial Dehn twist of a compact surface with boundary is the lifting of a half-twist in the braid
group , with respect to a suitable branched covering . In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on is a branched covering of
UNIVERSAL LEFSCHETZ FIBRATIONS AND LEFSCHETZ COBORDISMS
Full text linkWe 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. 55R55; 57R90, 57N1
On smooth functions with two critical values
Full text linkWe prove that every smooth closed connected manifold admits a smooth real-valued function with only two critical values such that the set of minima (or maxima) can be arbitrarily prescribed, as soon as this set is a finite subcomplex of the manifold (we call a function of this type a Reeb function). In analogy with Reeb’s Sphere Theorem, we use such functions to study the topology of the underlying manifold. In dimension 3, we give a characterization of manifolds having a Heegaard splitting of genus g in terms of the existence of certain Reeb functions. Similar results are proved in dimension n≥5
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