Modular frobenius manifolds and their invariant flows

Morrison, E.K. and Strachan, I. (2010) Modular frobenius manifolds and their invariant flows. International Mathematics Research Notices, 2011(17), pp. 3957-3982. (doi: 10.1093/imrn/rnq236)

Abstract

The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map I which sends a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may construct a so-called almost dual Frobenius manifold which satisfies almost all of the axioms of a Frobenius manifold. The action of I on the almost dual manifolds is studied, and the action of I on objects such as periods, twisted periods, and flows is studied. A distinguished class of Frobenius manifolds sit at the fixed point of this involutive symmetry, and this is made manifest in certain modular properties of the various structures. In particular, up to a simple reciprocal transformation, for this class of modular Frobenius manifolds, the flows are invariant under the action of I.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Strachan, Professor Ian
• Authors: Morrison, E.K., and Strachan, I.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Copyright Holders: Copyright © 2010 Oxford University Press
• First Published: First published in Advanceds in Mathematics 2010 2011(17):3957-3982
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher