The pre-WDVV ring of physics and its topology

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2 Scopus citations


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 Δ 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.

Original languageEnglish
Pages (from-to)269-281
Number of pages13
JournalRamanujan Journal
Issue number2
StatePublished - Oct 2005


  • Cohen-Macaulay
  • Keel's presentation
  • Moduli space
  • Morse matching
  • Pre-WDVV complex
  • WDVV equations
  • Whitehouse complex

ASJC Scopus subject areas

  • Algebra and Number Theory


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