The pre-WDVV ring of physics and its topology

Abstract

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex ${\Delta }_n$ is homotopy equivalent to a wedge of $(n-2)!$ spheres of dimension $n-4$. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex and the Hilbert series of the associated pre-WDVV ring.

13 pages, 4 figures, 2 tables

References in corpus (4)

• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Quantum Cohomology of a Product
• New moduli spaces of pointed curves and pencils of flat connections
• Complexes of connected graphs

Cited by in corpus (2)

• Tree homology and a conjecture of Levine
• Homotopy invariants for ${\overline{\mathcal{M}}}_{0,n}$ via Koszul duality