The APS-Theorem for general geometric operators

20.04.2023, 16:00  –  Raum 0.14
Forschungsseminar Differentialgeometrie

Alberto Richtsfeld (UP)

The APS theorem is the extension of the Atiyah-Singer index theorem to manifolds with boundary. While the Atiyah-Singer index theorem holds for all elliptic differential operators, the APS theorem in its original form has the restriction that it only holds for Dirac-type operators. Melrose introduced the b-category, which can be viewed as the category of manifolds with cylindrical ends, and gave an alternative proof of the APS theorem in this category, which was extended by Piazza to b-pseudodifferential operators. We will see that the methods developed by Bär and Bandara allow us to reduce Piazza's formula to manifolds with boundary in the case where the operator in question is a first-order geometric differential operator, such as the Rarita-Schwinger operator.