PIRSA:18080079

A natural refinement of the Euler characteristic

Wendland, K. (2018). A natural refinement of the Euler characteristic . Perimeter Institute. https://pirsa.org/18080079

Wendland, Katrin. A natural refinement of the Euler characteristic . Perimeter Institute, Aug. 17, 2018, https://pirsa.org/18080079 

          @misc{ pirsa_PIRSA:18080079,
            doi = {10.48660/18080079},
            url = {https://pirsa.org/18080079},
            author = {Wendland, Katrin},
            keywords = {Mathematical physics},
            language = {en},
            title = { A natural refinement of the Euler characteristic },
            publisher = {Perimeter Institute},
            year = {2018},
            month = {aug},
            note = {PIRSA:18080079 see, \url{https://pirsa.org}}
          }

Katrin Wendland

Albert-Ludwig Universität Freiburg

Talk number
PIRSA:18080079
Collection
Talk Type
Subject
Abstract
The Euler characteristic of a compact complex manifold M is a classical cohomological invariant. Depending on the viewpoint, it is most natural to interpret it as an index of an elliptic differential operator on M, or as a supersymmetric index in superconformal field theories “on M”. Refining the Euler characteristic but keeping with both index theoretic interpretations, one arrives at the notion of complex elliptic genera. We argue that superconformal field theory motivates further refinements of these elliptic genera which result in a choice of several new invariants, all of which have lost their interpretation in terms of index theory. However, at least if M is a K3 surface, then superconformal field theory and higher algebra select the same new invariant as a natural refinement of the complex elliptic genus.