Whitney tower concordance of classical links

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato-Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the 4-ball bounded by a link in the 3-sphere. Applications include computation of the grope filtration, and new geometric characterizations of Milnor's link invariants.Comment: Only change is the addition of this comment: This paper subsumes the entire preprint "Geometric Filtrations of Classical Link Concordance" (arXiv:1101.3477v2 [math.GT]) and the first six sections of the preprint "Universal Quadratic Forms and Untwisting Whitney Towers" (arXiv:1101.3480v2 [math.GT]

CP2\mathbb{CP}^2-stable classification of 44-manifolds with finite fundamental group

We show that two closed, connected $4$-manifolds with finite fundamental groups are $\mathbb{CP}^2$-stably homeomorphic if and only if their quadratic $2$-types are stably isomorphic and their Kirby-Siebenmann invariant agrees

Homotopy versus isotopy: spheres with duals in 4-manifolds

David Gabai recently proved a smooth 4-dimensional "Light Bulb Theorem" in the absence of 2-torsion in the fundamental group. We extend his result to 4-manifolds with arbitrary fundamental group by showing that an invariant of Mike Freedman and Frank Quinn gives the complete obstruction to "homotopy implies isotopy" for embedded 2-spheres which have a common geometric dual. The invariant takes values in an Z/2Z-vector space generated by elements of order 2 in the fundamental group and has applications to unknotting numbers and pseudo-isotopy classes of self-diffeomorphisms. Our methods also give an alternative approach to Gabai's theorem using various maneuvers with Whitney disks and a fundamental isotopy between surgeries along dual circles in an orientable surface

The round handle problem

We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-manifold R constructed from adding round handles to the four ball. A negative answer would contradict the union of the surgery conjecture and the s-cobordism conjecture for 4-manifolds with free fundamental group

Kinetic study of the selective hydrogenation of styrene over a Pd egg-shell composite catalyst

This is a study on the kinetics of the liquid-phase hydrogenation of styrene to ethylbenzene over a catalyst of palladium supported on an inorganic–organic composite. This support has a better mechanical resistance than other commercial supports, e.g. alumina, and yields catalysts with egg-shell structure and a very thin active Pd layer. Catalytic tests were carried out in a batch reactor by varying temperature, total pressure and styrene initial concentration between 353–393 K, 10–30 bar, and 0.26–0.60 mol L−1. Kinetic models were developed on the assumptions of dissociative hydrogen chemisorption and non-negligible adsorption of hydrogen and styrene. Final chemical reaction expressions useful for reactor design were obtained. The models that best fitted the experimental data were those ones that considered the surface reaction as the limiting step. In this sense, a two-step Horiuti–Polanyi working mechanism with half hydrogenation intermediates gave the best fit of the experimental data. The heats of adsorption of styrene and ethylbenzene were also estimated.The authors are gratefully indebted to CONICET, ANPCyT and Universidad Nacional del Litoral for financially sponsoring this research work