New invariants of G2–structures

By D. Crowley, Johannes Nordstrom. 2012

59 citations recorded by the source corpus.

We define a Z/48-valued homotopy invariant nu of a G_2-structure on the tangent bundle of a closed 7-manifold in terms of the signature and Euler characteristic of a coboundary with a Spin(7)-structure. For manifolds of holonomy G_2 obtained by the twisted connected sum construction, the associated torsion-free G_2-structure always has nu = 24. Some holonomy G_2 examples constructed by Joyce by desingularising orbifolds have odd nu. We define a further homotopy invariant xi of G_2-structures such that if M is 2-connected then the pair (nu, xi) determines a G_2-structure up to homotopy and diffeomorphism. The class of a G_2-structure is determined by nu on its own when the greatest divisor of p_1(M) modulo torsion divides 224; this sufficient condition holds for many twisted connected sum G_2-manifolds. We also prove that the parametric h-principle holds for coclosed G_2-structures.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/84999babbec17d748d6d8b8032ae18f304b03320

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In Discrete Mathematics and Combinatorics

D. Joyce

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi–Hanson spaces (2017, background): “(iv) New topological and analytic invariants of G2-structures have been introduced by Crowley–Nordström [8] and Crowley–Goette–Nordström [9].”