Elliptic operators and uniform K-homology

05.06.2025, 16:15  –  Raum 1.22
Forschungsseminar Differentialgeometrie

Lyko Matti (Greifswald)

Analytic K-homology is a homology theory whose cycles are elliptic operators, and as such is a useful tool around which to organize index calculations on compact manifolds. On non-compact manifolds the index of an elliptic operator need not exist, but its K-homology class can still be defined. As a topological invariant, however, K-homology contains no metric information. As this information is useful in a geometric context, uniform K-homology, a metric-sensitive modification of analytic K-homology, is introduced and it is proved that suitably uniform elliptic operators define classes in it. Particular focus is put on elliptic operators on manifolds with boundary.