Tops as Building Blocks for G2 Manifolds

Abstract

A large number of examples of compact $G_2$ manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two appropriate building blocks times a circle. These building blocks, which are appropriate $K3$-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes.

43 pages, v2: typos corrected, improved discussion, references added, v3: reorganized and improved parts of the discussion, fixed typos

References in corpus (2)

• The Landscape of M-theory Compactifications on Seven-Manifolds with $G_2$ Holonomy
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces

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