Topological toric manifolds
By Hiroaki Ishida, Yukiko Fukukawa, M. Masuda. 2010
60 citations recorded by the source corpus.
We introduce the notion of a topological toric manifold and a topological fan and show that there is a bijection between omnioriented topological toric manifolds and complete non-singular topological fans. A topological toric manifold is a topological analogue of a toric manifold and the family of topological toric manifolds is much larger than that of toric manifolds. A topological fan is a combinatorial object generalizing the notion of a simplicial fan in toric geometry. Prior to this paper, two topological analogues of a toric manifold have been introduced. One is a quasitoric manifold and the other is a torus manifold. One major difference between the previous notions and topological toric manifolds is that the former support a smooth action of an $S^1$-torus while the latter support a smooth action of a $\C^*$-torus. We also discuss their relation in details.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/71f0d278214e9a74cbb317fb44e809fc7c75fb4b
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In Algebra and Number Theory
In Computational Theory and Mathematics
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Citations in the corpus
- On the cohomology and their torsion of real toric objects (2013, background): “Furthermore, it is shown by [11] that M(K,λ) is Davis-Januszkiewicz equivalent to M .”
- Rigidity problems in toric topology: A survey (2011, background): “ation spaces of (C∗)n. To a topological toric manifold X, one can associate a combinatorial object ∆(X) called a complete non-singular topological fan similarly to the toric case. The main theorem in [28] says that the correspondence X → ∆(X) is a bijection between topological toric manifolds and co”
- Toric Topology (2012, methodology): “As is pointed out in [170], keeping only the first part of the definition (i.”