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5-th Conference on Geometry and Topology of Manifolds
April 27 - May 3, 2003

Krynica, Poland

Organizers
Institute of Mathematics of the Technical University of Lodz; Institute of Mathematics of the Jagiellonian University, Cracow; Faculty of Applied Mathematics of the University Mining and Matallurgy, Cracow

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Second neighbourhood of the diagonal, and a foundation for conformal geometry
by
Anders Kock
University of Aarhus, Denmark

A Riemannian metric on a manifold M gives rise to a structure of combinatorial character on the manifold, namely a "Laplacian" neigbourhood ML of the diagonal. It lies in between the classical first and second neighbourhood of the diagonal. In terms of this ML, conformal maps may be characterized as those maps that preserve Laplacian neighbourhoods. Our description is a simplification of the original one, as provided in our ''Infinitesimal aspects of the Laplace Operator", Theory and Applications of Categories Vol. 9 (2001).

Date received: April 9, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakm-12.