TL;DR
This paper explores the geometric and topological properties of 8-dimensional Spin(7) manifolds, focusing on 4-planes, differential forms, and mirror duality, to deepen understanding of their symmetries and structures.
Contribution
It introduces a detailed analysis of 4-planes and differential forms in Spin(7) manifolds, and investigates mirror duality and its topological implications.
Findings
Characterization of 4-planes in Spin(7) manifolds
Analysis of Cayley 4-form and Spin(7) actions
Conditions for mirror duality in exceptional holonomy
Abstract
This paper investigates the geometric structures and properties of 8-dimensional manifolds with Spin(7)-holonomy. We focus on the characterization and implications of 4-planes within these manifolds, which are endowed with an almost symplectic structure compatible with the Spin(7)-structure. We provide a detailed analysis of the differential forms defining these structures, including the Cayley 4-form and its stabilization under the Spin(7) group actions. Furthermore, we explore the concept of mirror duality within the context of exceptional holonomy, elucidating the relationship between dual structures and their topological constraints. By examining the conditions under which mirror duality arises, we enhance the understanding of the interplay between Spin(7)-structures and symplectic geometry. This endeavor contributes to our deeper understanding of the intricate symmetries and…
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic and Geometric Analysis · Homotopy and Cohomology in Algebraic Topology