Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology, quantum fields theory and cosmology.

Readership : Graduate students and researchers in theoretical and mathematical physics, Cosmology as well as geometry and topology.

La géométrie différentielle et la topologie sont devenues aujourd'hui des outils essentiels en physique. En particulier, elles sont indispensables dans les études théoriques portant sur la physique des matières condensées, la gravitation, et la physique des particules.
Ce volume offre une introduction aux développements récents dans divers domaines de recherche à l'interface entre la géométrie, topologie, théorie quantique des champs et cosmologie.

Ce livre s'adresse à des étudiants et des chercheurs en physique théorique et mathématiques, en cosmologie, ainsi qu'en géométrie et topologie.

Auteurs : Jean-Michel Alimi, Abhay Ashtekar, Philippe Brax, Carsten van de Bruck, Anne-Christine David, Nicolas Franco, André Fûzfa, Eduardo Guendelman, Frédéric Hélein, Alex Kaganovich, Nabil Khouadji, Joseph Kouneiher, David Langlois. Philippe G. LeFloch, Fedele Lizzi, Jean-Pierre Luminet, Sylvain Maillot, Ghani Zeghib.

• The issue of the beginning in quantum gravity
• Manifolds obtained by soldering together points, lines, etc.
• Energy-momentum's local conservation laws and generalized isometric embeddings of vector bundles
• Local canonical foliations of lorentzian manifolds with bounded curvature
• Ricci flow, scalar curvature and the poincare conjecture
• Dynamical systems, einstein flow and geometrization
• Physical consequences of a theory with dynamical volume element
• Topology and cosmology
• An introduction to the abnormally weighting energy hypothesis and non-universal tensor-scalar gravitation
• Early universe : inflation and cosmological perturbations
• Fermionic zero modes of cosmic strings
• The structure of gravity in non-commutative geometry
• Survey of gravity in non-commutative geometry