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- Norbert Poncin, Fabian Radoux, Robert Wolak
- 2008

Many mathematical models of physical phenomena that have been proposed in recent years require more general spaces than manifolds. When taking into account the symmetry group of the model, we get a reduced model on the (singular) orbit space of the symmetry group action. We investigate quantization of singular spaces obtained as leaf closure spaces of… (More)

A family of probability distributions parametrized by an open domain Λ in Rn defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix is positive definite defining in this way a Riemannian metric on Λ. If we replace the "positive… (More)

- Martintxo Saralegi-Aranguren, Robert Wolak
- 2005

We study the cohomology properties of the singular foliation F determined by an action Φ: G×(M,μ) → (M,μ) where the abelian Lie group G preserves the riemannien metric μ on the compact manifold M . More precisely, we prove that the basic intersection cohomology IH ∗ p (M/F) is finite dimensional and verifies the Poincaré Duality. This duality includes two… (More)

- Jerzy J. Konderak, Robert A. Wolak, Jerzy J. KONDERAK, Robert A. WOLAK
- 2002

We consider leaf preserving maps between manifolds equipped with Riemannian foliations. We construct a transversal tension field for such maps and define transversally harmonic maps. Then we give some examples of such maps using the suspension construction.

- Robert Wolak
- 2008

In the paper we introduce the notions of a singular fibration and a singular Seifert fibration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For singular foliations defined by such fibrations we prove a de Rham type theorem for the basic intersection cohomology… (More)

- Michel Nguiffo Boyom, Robert Wolak
- GSI
- 2013

- José Ignacio Royo Prieto, Robert Wolak
- 2005

For a riemannian foliation F on a closed manifold M , it is known that F is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form κμ (relatively to a suitable riemannian metric μ) is zero (cf. [1]). In the transversally orientable case, tautness is equivalent to the non-vanishing of the top… (More)

- ROBERT A. WOLAK
- 2006

ROBERT A. WOLAK In Chis short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation or equivalently the space of leaves of such a foliation is a Satake manifold . A particular attention is paid to transversely affine foliations . We present several conditions such ensure completeness of… (More)

- Martintxo Saralegi-Aranguren, Robert Wolak
- 2012

We prove that the basic intersection cohomology IH ∗ p (M/F ), where F is the singular foliation determined by an isometric action of a Lie group G on the compact manifold M, is finite dimensional. This paper deals with an action Φ : G × M → M of a Lie group on a compact manifold preserving a riemannian metric on it. The orbits of this action define a… (More)

- Robert A. Wolak
- 2003

We study the geometry of the leaf closure space of regular and singular Riemannian foliations. We give conditions which assure that this leaf space is a singular symplectic or Kähler space. In recent years physicists and mathematicians working on mathematical models of physical phenomena have realised that modelling based on geometric structures on now… (More)