Notes on the octonions
Dietmar A. Salamon, Thomas Walpuski
TL;DR
This paper explains the linear algebra foundational to Donaldson-Thomas theory and the geometry of special holonomy manifolds, focusing on octonions and their role in these advanced mathematical topics.
Contribution
It provides an expository overview of the linear algebra related to octonions, Donaldson-Thomas theory, and special holonomy manifolds, clarifying complex concepts for researchers.
Findings
Clarifies the role of octonions in special holonomy geometry
Connects linear algebra to Donaldson-Thomas invariants
Provides foundational insights for further research
Abstract
This is an expository paper. Its purpose is to explain the linear algebra that underlies Donaldson-Thomas theory and the geometry of Riemannian manifolds with holonomy in and .
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Algebra and Geometry