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Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras

Johannes Huebschmann (2000)

Banach Center Publications

Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential) G-algebra...

Diffusion to infinity for periodic orbits in meromorphic dynamics

Janina Kotus, Grzegorz Świątek (2002)

Fundamenta Mathematicae

A small perturbation of a rational function causes only a small perturbation of its periodic orbits. We show that the situation is different for transcendental maps. Namely, orbits may escape to infinity under small perturbations of parameters. We show examples where this "diffusion to infinity" occurs and prove certain conditions under which it does not.

Dimension algébrique de sous-groupes analytiques de variétés de groupe

Michel Waldschmidt (1975)

Annales de l'institut Fourier

Soient G une variété de groupe définie sur le corps Q ‾ des nombres algébriques, et φ : C n → G C un sous-groupe à n paramètres de G , de dimension algébrique d . Nous nous proposons de majorer le rang ℓ (sur Z ) des sous-groupes Γ de C n dont l’image par φ est contenue dans le groupe G Q ‾ des points algébriques de G .E. Bombieri et S. Lang ont déjà obtenu de telles majorations, en supposant que les points de Γ sont très bien distribués : pour d ≥ n + 1 , on a ℓ ≤ n 2 + 3 n pour des variétés linéaires, et ℓ ≤ 2 n 2 + 4 n pour des variétés abéliennes .Nous...

Dimension vs. genus: A surface realization of the little k-cubes and an E ∞ operad

Ralph M. Kaufmann (2009)

Banach Center Publications

We define a new E ∞ operad based on surfaces with foliations which contains E k suboperads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes (thus making contact with string topology), by giving explicit cell representatives for the Dyer-Lashof-Cohen operations for the 2-cubes and by constructing new Ω spectra. The underlying novel principle is that we can trade genus in the surface representation vs. the dimension k of the little...

Directional properties of sets definable in o-minimal structures

Satoshi Koike, Ta Lê Loi, Laurentiu Paunescu, Masahiro Shiota (2013)

Annales de l’institut Fourier

In a previous paper by Koike and Paunescu, it was introduced the notion of direction set for a subset of a Euclidean space, and it was shown that the dimension of the common direction set of two subanalytic subsets, called the directional dimension, is preserved by a bi-Lipschitz homeomorphism, provided that their images are also subanalytic. In this paper we give a generalisation of the above result to sets definable in an o-minimal structure on an arbitrary real closed field. More precisely, we...

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