Abstract:[nl]
I will discuss a replacement for homotopy cardinality in situations where it is a priori ill-defined, including Z/2-graded dg-categories. A key ingredient are Calabi-Yau structures and their relative generalizations. As an application we obtain a Hall algebra for many pre-triangulated dg-categories for which it was previously undefined. Another application is the proof of a conjecture of Ng-Rutherford-Shende-Sivek expressing the ruling polynomial of a Z/2m-graded Legendrian knot (which is part of the HOMFLY polynomial if m=1) in terms of the homotopy cardinality of its augmentation category. All this is joint work with Mikhail Gorsky.
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- Organizer: Centre for Quantum Mathematics
- Address: Campusvej 55, 5230 Odense M
- Contact Email: qm@sdu.dk
- Add to your calendar: https://eom.sdu.dk:443/events/ical/92eca0e3-ebe4-4f83-8d4c-0eb0deb254b8