The pre-WDVV ring of physics and its topology

Margaret A. Readdy

doi:10.1007/s11139-005-4850-1

The pre-WDVV ring of physics and its topology

Margaret A. Readdy

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	269-281
Number of pages	13
Journal	Ramanujan Journal
Volume	10
Issue number	2
DOIs	https://doi.org/10.1007/s11139-005-4850-1
State	Published - Oct 2005

Keywords

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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10.1007/s11139-005-4850-1

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AB - 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.

KW - Cohen-Macaulay

KW - Keel's presentation

KW - Moduli space

KW - Morse matching

KW - Pre-WDVV complex

KW - WDVV equations

KW - Whitehouse complex

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VL - 10

SP - 269

EP - 281

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

ER -

The pre-WDVV ring of physics and its topology

Abstract

Keywords

ASJC Scopus subject areas

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