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Hasse diagrams for parabolic geometries

Krump, Lukáš, Souček, Vladimír (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

The invariant differential operators on a manifold with a given parabolic structure come in two classes, standard and non-standard, and can be further subdivided into regular and singular ones. The standard regular operators come in repeated patterns, the Bernstein-Gelfand-Gelfand sequences, described by Hasse diagrams. In this paper, the authors present an alternative characterization of Hasse diagrams, which is quite efficient in the case of low gradings. Several examples are given.

Hecke operators on de Rham cohomology.

Min Ho Lee (2004)

Revista Matemática Complutense

We introduce Hecke operators on de Rham cohomology of compact oriented manifolds. When the manifold is a quotient of a Hermitian symmetric domain, we prove that certain types of such operators are compatible with the usual Hecke operators on automorphic forms.

Homotopy algebras via resolutions of operads

Markl, Martin (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Summary: All algebraic objects in this note will be considered over a fixed field k of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over k . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by J. P. May [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [J.-L. Loday, “La renaissance des opérads”, Sémin. Bourbaki 1994/95,...

Homotopy type of Euclidean configuration spaces

Salvatore, Paolo (2001)

Proceedings of the 20th Winter School "Geometry and Physics"

Let F ( ℝ n , k ) denote the configuration space of pairwise-disjoint k -tuples of points in ℝ n . In this short note the author describes a cellular structure for F ( ℝ n , k ) when n ≥ 3 . From results in [F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of F ( ℝ n , k ) is well-understood. This allows an identification of the location of the cells of F ( ℝ n , k ) in a minimal cell decomposition. Somewhat more detail is provided by the main result here,...

Impossible Einstein-Weyl geometries

Eastwood, Michael (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.

Integrability of the Poisson algebra on a locally conformal symplectic manifold

Haller, Stefan, Rybicki, Tomasz (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Summary: It is proven that the Poisson algebra of a locally conformal symplectic manifold is integrable by making use of a convenient setting in global analysis. It is also observed that, contrary to the symplectic case, a unified approach to the compact and non-compact case is possible.

Introduction

J. C. Saut, R. Temam (1989)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Introduction

John Oprea, Aleksy Tralle (1998)

Banach Center Publications

Invariance properties of the Laplace operator

Eichhorn, Jürgen (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The paper deals with a special problem of gauge theory. In his previous paper [The invariance of Sobolev spaces over noncompact manifolds, Partial differential equations, Proc. Symp., Holzhaus/GDR 1988, Teubner- Texte Math. 112, 73-107 (1989; Zbl 0681.58011)], the author introduced the Sobolev completions 𝒞 ¯ P k of the space 𝒞 P of all G-connections on a G-principal fibre bundle P. In the present paper, under the assumption of bounded curvatures and their...

Invariant orders in Lie groups

Neeb, Karl-Hermann (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group G admits a continuous invariant order if and only if its Lie algebra L ( G ) contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If G is solvable and simply connected then all pointed invariant cones W in L ( G ) are global in G (a Lie wedge W ⊂ L ( G ) is said to...

Isometric immersions and induced geometric structures

D‘Ambra, G. (1999)

Proceedings of the 18th Winter School "Geometry and Physics"

In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.

Currently displaying 61 – 80 of 190