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Special Holonomy on Special Spaces

2014/03/06 by Manuel Amann, Amann, Manuel
Mathematics · Physics and Astronomy · #53C29 (Primary) #55P15 #57N65 (Secondary) #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Noncommutative and Quantum Gravity Theories #math.AT #math.DG #msc:53C29 #msc:55P15 #msc:57N65

paper · pdf · doi:10.48550/arxiv.1403.1442

arxiv created 2014/03/06 · openalex publication_date 2014/03/06 · arxiv updated 2014/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterise simply-connected biquotients which potentially admit metrics of holonomy G2. We prove that there are at most three real homotopy types of rationally elliptic such manifolds---all of them being formal. In the course of this examination we classify rationally elliptic homotopy types and characterise 7-dimensional simply-connected biquotients from a rational point of view. Moreover, we also investigate further manifolds of special holonomy, like manifolds of holonomy Spin(7) or Sp(n)\Sp(1) in special situations provided by rational ellipticity or geometric formality.

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