Analogues of Euler characteristic
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Mon, 01/11/2010 15:45 |
Tom Leinster (Glasgow) |
Topology Seminar  |
L3 |
| There is a close but underexploited analogy between the Euler characteristic of a topological space and the cardinality of a set. I will give a quite general definition of the "magnitude" of a mathematical structure, framed categorically. From this single definition can be derived many cardinality-like invariants (some old, some new): the Euler characteristic of a manifold or orbifold, the Euler characteristic of a category, the magnitude of a metric space, the Euler characteristic of a Koszul algebra, and others. A conjecture states that this purely categorical definition also produces the classical invariants of integral geometry: volume, surface area, perimeter, .... No specialist knowledge will be assumed. | |||