The pre-WDVV ring of physics and its topology

Details The pre-WDVV ring of physics and its topology The pre-WDVV ring of physics and its topology

2005-11-16

arxiv.org/abs/math/0511420v1

Ramanujan J 10 (2005), 269-281

Mathematics

Combinatorics

13 pages, 4 figures, 2 tables

Scientific paper

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.

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