Abstract
The fact that ℝ2 possesses a complex multiplication making it into a field has important applications, leading for example to the theory of Riemann surfaces. Similarly, the quaternion multiplication on ℝ4 has important applications to the geometry of four-manifolds. In four dimensions, quaternions yield a simplification of the theory of spinors (which is presented in full generality in the highly recommended references [25] and [4]).
Keywords
- Vector Bundle
- Line Bundle
- Dirac Operator
- Clifford Algebra
- Spin Manifold
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2001). Spin geometry on four-manifolds. In: Lectures on Seiberg-Witten Invariants. Lecture Notes in Mathematics, vol 1629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40952-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-40952-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41221-2
Online ISBN: 978-3-540-40952-6
eBook Packages: Springer Book Archive
