Donaldson theory

Donaldson theory is the study of smooth 4-manifolds using gauge theory. It was started by Simon Donaldson (1983) who proved Donaldson's theorem restricting the possible quadratic forms on the second cohomology group of a compact simply connected 4-manifold.

Most of the results of Donaldson theory depend on the manifold having a differential structure, and are false for topological 4-manifolds.

Many of the theorems in Donaldson theory can now be proved more easily using Seiberg–Witten theory.

References

• Donaldson, Simon (1983), "An Application of Gauge Theory to Four Dimensional Topology", Journal of Differential Geometry 18 (2): 279–315, MR710056 .
• Donaldson, S. K.; Kronheimer, P. B. (1997), The Geometry of Four-Manifolds, Oxford Mathematical Monographs, Oxford: Clarendon Press, ISBN 0198502699 .
• Freed, D. S.; Uhlenbeck, K. K. (1984), Instantons and four-manifolds, New York: Springer, ISBN 0387960368 .
• Scorpan, A. (2005), The wild world of 4-manifolds, Providence: American Mathematical Society, ISBN 0821837494 .

This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometric topology 4-manifolds Differential topology Topology stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Fernando Chamorro Everard Mott Williams Look at other dictionaries: Donaldson–Thomas theory — In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants. Given a compact moduli space of sheaves on a Calabi–Yau threefold, its Donaldson–Thomas invariant is the virtual number of its… …   Wikipedia Donaldson's theorem — In mathematics, Donaldson s theorem states that a definite intersection form of a simply connected smooth manifold of dimension 4 is diagonalisable. If the intersection form is positive (negative) definite, it can be diagonalized to the identity… …   Wikipedia Simon Donaldson — Infobox Scientist name = Simon Kirwan Donaldson box width = image width = caption = birth date = birth date and age|1957|08|20 birth place = Cambridge, England death date = death place = residence = citizenship = nationality = flagicon|UK British …   Wikipedia Stewart Donaldson — is Professor and Chair of Psychology, Director of the Institute of Organizational and Program Evaluation Research, and Dean of the School of Behavioral and Organizational Sciences (SBOS), Claremont Graduate University in Claremont, California. He …   Wikipedia Stakeholder theory — The stakeholder theory is a theory of organizational management and business ethics that addresses morals and values in managing an organization. [Cite book |last=Phillips, R. |first=Robert |coauthors=Edward Freeman |title=Stakeholder Theory and… …   Wikipedia Simon Donaldson — Simon Kirwan Donaldson (* 20. August 1957 in Cambridge) ist ein englischer Mathematiker, der vor allem für seine Arbeiten zur Topologie vierdimensionaler Mannigfaltigkeiten bekannt ist. Inhaltsverzeichnis 1 Leben 2 Auszeichnungen 3 …   Deutsch Wikipedia Simon K. Donaldson — Simon Kirwan Donaldson (* 20. August 1957 in Cambridge) ist ein englischer Mathematiker, der vor allem für seine Arbeiten zur Topologie vierdimensionaler Mannigfaltigkeiten bekannt ist. Inhaltsverzeichnis 1 Leben 2 Auszeichnungen 3 Schriften …   Deutsch Wikipedia Stephen Donaldson (activist) — Stephen Donaldson Stephen Donaldson, July 1995 Born Robert Anthony Martin, Jr July 27, 1946(1946 07 27) Utica, New York, U.S. Died July 18, 19 …   Wikipedia Gauge theory — For a generally accessible and less technical introduction to the topic, see Introduction to gauge theory. In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations …   Wikipedia Simon Donaldson — Pour les articles homonymes, voir Donaldson. Simon Kirwan Donaldson Naissance 20 août 1957 Cambridge (Angleterre) Domicile Royaume Uni Nationalité …   Wikipédia en Français 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”