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Coarse topology, enlargeability, and essentialness

Bernhard Hanke, Dieter Kotschick, John Roe, Thomas Schick (2008)

Annales scientifiques de l'École Normale Supérieure

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K -theory of the corresponding reduced C * -algebras. Our proofs do not depend on the Baum–Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.

Cocalibrated G 2 -manifolds with Ricci flat characteristic connection

Thomas Friedrich (2013)

Communications in Mathematics

Any 7-dimensional cocalibrated G 2 -manifold admits a unique connection ∇ with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the ∇ -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of ∇ -parallel vector fields.

Codimension one foliations on complex tori

Marco Brunella (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.

Codimension one minimal foliations and the fundamental groups of leaves

Tomoo Yokoyama, Takashi Tsuboi (2008)

Annales de l’institut Fourier

Let ℱ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold M . We show that if the fundamental group of each leaf of ℱ is isomorphic to Z , then ℱ is without holonomy. We also show that if π 2 ( M ) ≅ 0 and the fundamental group of each leaf of ℱ is isomorphic to Z k ( k ∈ Z ≥ 0 ), then ℱ is without holonomy.

Codimension one symplectic foliations.

Omegar Calvo, Vicente Muñoz, Francisco Presas (2005)

Revista Matemática Iberoamericana

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.

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