Matrix factorisation of Morse-Bott functions

7 June 2016
15:45
Constantin Teleman
Abstract

For a holomorphic function (“superpotential”)  W: X —> C on a complex manifold X, one defines the (2-periodic) matrix factorisation category MF(X;W), which is supported on the critical locus Crit(W) of W. At a Morse singularity, MF(X;W) is equivalent to the category of modules over the Clifford algebra on the tangent space TX. It had been suggested by Kapustin and Rozansky that, for Morse-Bott W, MF(X;W) should be equivalent to the (2-periodicised) derived category of Crit(W), twisted by the Clifford algebra of the normal bundle. I will discuss why this holds when the first neighbourhood of Crit(W) splits, why it fails in general, and will explain the correct general statement.

  • Algebraic and Symplectic Geometry Seminar