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Charles Ehresmann's concepts in differential geometry

Paulette Libermann (2007)

Banach Center Publications

We outline some of the tools C. Ehresmann introduced in Differential Geometry (fiber bundles, connections, jets, groupoids, pseudogroups). We emphasize two aspects of C. Ehresmann's works: use of Cartan notations for the theory of connections and semi-holonomic jets.

Cheeger inequalities for unbounded graph Laplacians

Frank Bauer, Matthias Keller, Radosław K. Wojciechowski (2015)

Journal of the European Mathematical Society

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

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