Journal of Symplectic Geometry

Volume 15 (2017)

Number 2

Strings, fermions and the topology of curves on annuli

Pages: 421 – 506



Daniel V. Mathews (School of Mathematical Sciences, Monash University, Clayton, Victoria, Australia)


In previous work with Schoenfeld, we considered a string-type chain complex of curves on surfaces, with differential given by resolving crossings, and computed the homology of this complex for discs.

In this paper we consider the corresponding “string homology” of annuli. We find this homology has a rich algebraic structure which can be described, in various senses, as fermionic. While for discs we found that an isomorphism between string homology and the sutured Floer homology of a related $3$-manifold, in the case of annuli we find the relationship is more complex, with string homology containing further higher-order structure.

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Paper received on 12 December 2014.