In mathematics, a toric manifold is a topological analogue of toric variety in algebraic geometry. It is an even-dimensional manifold with an effective smooth action of an -dimensional compact torus which is locally standard with the orbit space a simple convex polytope.[1][2]
The aim is to do combinatorics on the quotient polytope and obtain information on the manifold above. For example, the Euler characteristic and the cohomology ring of the manifold can be described in terms of the polytope.
YouTube Encyclopedic
-
1/3Views:311663431
-
Localizing the Fukaya category of a Weinstein manifold - Ganatra
-
Lagrangian Floer homology
-
Group actions on b-symplectic manifolds (Victor Guillemin)
Transcription
The Atiyah and Guillemin-Sternberg theorem
This theorem states that the image of the moment map of a Hamiltonian toric action is the convex hull of the set of moments of the points fixed by the action. In particular, this image is a convex polytope.
References
- ^ Jeffrey, Lisa C. (1999), "Hamiltonian group actions and symplectic reduction", Symplectic geometry and topology (Park City, UT, 1997), IAS/Park City Math. Ser., vol. 7, Amer. Math. Soc., Providence, RI, pp. 295–333, MR 1702947.
- ^ Masuda, Mikiya; Suh, Dong Youp (2008), "Classification problems of toric manifolds via topology", Toric topology, Contemp. Math., vol. 460, Amer. Math. Soc., Providence, RI, pp. 273–286, arXiv:0709.4579, doi:10.1090/conm/460/09024, MR 2428362.
 | This algebraic geometry–related article is a stub. You can help Wikipedia by expanding it. |
This page was last edited on 8 July 2021, at 20:23