Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 4

Fukaya $A_{\infty}$-categories associated to Lefschetz fibrations. II ½

Pages: 883 – 944



Paul Seidel (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


We consider a version of the relative Fukaya category for anti-canonical Lefschetz pencils. There are direct connections between the behaviour of this category and enumerative geometry: some of these are results announced here, others remain conjectural. Among the conjectural goals is a formula for the dependence of the Fukaya category of Calabi–Yau hypersurfaces on the Novikov (area) parameter.

Published 4 November 2016