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The Pre-WDVV Ring of Physics and its Topology

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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 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, Kentucky, 40506-0027

    Margaret A. Readdy

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  1. Margaret A. Readdy
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Correspondence to Margaret A. Readdy.

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2000 Mathematics Subject Classification: Primary—13F55, Secondary—05E99, 55P15

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Readdy, M.A. The Pre-WDVV Ring of Physics and its Topology. Ramanujan J 10, 269–281 (2005). https://doi.org/10.1007/s11139-005-4850-1

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  • DOI: https://doi.org/10.1007/s11139-005-4850-1

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