On the eta invariant of (2,3,5) distributions

2025/04/25 by Stefan Haller, Haller, Stefan · 1 citation
Mathematics · #11M41 #53C17 #58A30 #58J10 #58J28 (primary) and 11M35 #58J42 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2504.18417

openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Rumin complex associated with a generic rank two distribution on a closed 5-manifold. The Rumin differential in middle degrees gives rise to a self-adjoint differential operator of Heisenberg order two. We study the eta function and the eta invariant of said operator, twisted by unitary flat vector bundles. For (2,3,5) nilmanifolds this eta invariant vanishes but the eta function is nontrivial, in general. We establish a formula expressing the eta function of (2,3,5) nilmanifolds in terms of more elementary functions.

Citations

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Cited by

• Geometric aspects of rank-3 vector bundles over surfaces and 2-plane distributions on 5-manifolds

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