Conically singular Cayley submanifolds I: Deformations
Gilles Englebert
TL;DR
This paper develops the deformation theory for conically singular and asymptotically conical Cayley submanifolds, foundational for constructing fibrations of Spin(7) manifolds by Cayley submanifolds.
Contribution
It introduces the deformation theory framework for conically singular Cayley submanifolds, a key step towards fibration constructions in Spin(7) geometry.
Findings
Deformation theory for conically singular Cayley submanifolds established
Analysis of asymptotically conical Cayley submanifolds provided
Foundations for future fibration constructions laid out
Abstract
This is the first in a series of three papers working towards constructing fibrations of compact Spin(7) manifolds by Cayley submanifolds. In this paper we describe the deformation theory of conically singular and asymptotically conical Cayley submanifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Geometry and complex manifolds