Communications in Mathematical Physics

, Volume 352, Issue 1, pp 1–36 | Cite as

Spin(7)-Instantons, Cayley Submanifolds and Fueter Sections

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Abstract

We prove an existence theorem for Spin(7)-instantons, which are highly concentrated near a Cayley submanifold; thus giving a partial converse to Tian’s foundational compactness theorem (Ann Math (2) 151(1):193–268, 2000). As an application, we show how to construct Spin(7)-instantons on Spin(7)-manifolds with suitable local K3 Cayley fibrations. This recovers an example constructed by Lewis (Spin(7) instantons, Ph.D. Thesis, 1998).

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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