TL;DR
This paper introduces a novel construction method for compact G2 manifolds using tops, inspired by the reflexive polytope approach for Calabi-Yau manifolds, aiding in M-Theory compactifications.
Contribution
It establishes a new link between tops and G2 manifold construction, providing an elegant framework for building blocks in twisted connected sum methods.
Findings
Construction of G2 manifolds via tops is feasible and systematic.
Tops offer a parallel to reflexive polytopes in Calabi-Yau construction.
Enhanced understanding of G2 manifolds relevant to M-Theory compactifications.
Abstract
A large number of examples of compact 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 -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.
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