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Homotopy invariance of higher signatures and 3 -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3 -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable 3 -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients holds. The...

Hypercomplex Algebras and Geometry of Spaces with Fundamental Formof an Arbitrary Order

Mikhail P. Burlakov, Igor M. Burlakov, Marek Jukl (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.

Hypersurfaces in n and critical points in their external region

P. M. G. Manchón (2002)

Czechoslovak Mathematical Journal

In this paper we study the hypersurfaces M n given as connected compact regular fibers of a differentiable map f : n + 1 , in the cases in which f has finitely many nondegenerate critical points in the unbounded component of n + 1 - M n .

Hypersurfaces intégrales des feuilletages holomorphes

Felipe Cano, Jean-François Mattei (1992)

Annales de l'institut Fourier

Soit ω un germe en 0 C n de 1-forme différentielle holomorphe, satisfaisant la condition d’intégrabilité ω d ω = 0 et non dicritique, i.e. sur toute surface Z non intégrale de ω , on ne peut tracer, au voisinage de 0, qu’un nombre fini de germes de courbes analytiques ( Γ i , P i ) , intégrales de ω , avec P i Z Sing ω . Alors ω possède un germe d’hypersurface analytique intégrale.

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