Circle actions on six dimensional oriented manifolds with isolated fixed points
@inproceedings{Jang2021CircleAO, title={Circle actions on six dimensional oriented manifolds with isolated fixed points}, author={Donghoon Jang}, year={2021} }
Circle actions and torus actions on compact oriented 4manifolds were studied and classified in 1970’s but completely classifying those actions on 6-manifolds is challenging and known results on 6manifolds require strong assumptions on actions and/or manifolds. In this paper, we study circle actions on compact oriented 6-manifolds with finite fixed point sets. We show that for any such manifold, we can successively take equivariant connected sums at fixed points with S, CP, and 6-dimensional…
One Citation
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References
SHOWING 1-10 OF 34 REFERENCES
Circle actions on oriented manifolds with discrete fixed point sets and classification in dimension 4
- Mathematics, Computer ScienceJournal of Geometry and Physics
- 2018
Circle actions on four dimensional almost complex manifolds with discrete fixed point sets.
- Mathematics
- 2019
Let the circle act on a 4-dimensional compact almost complex manifold $M$ with a discrete fixed point set. Let us call the fixed point data of $M$ by the collection of multisets of weights at the…
Circle actions on almost complex manifolds with 4 fixed points
- MathematicsMathematische Zeitschrift
- 2019
Let the circle act on a compact almost complex manifold M . In this paper, we classify the fixed point data of the action if there are 4 fixed points and the dimension of the manifold is at most 6.…
Classification of the actions of the circle on 3-manifolds
- Mathematics
- 1968
(The manifold M6,g,h,t is an explicit sum of handles and p2 X S1's. The L'(Pt, v1)'s are lens spaces each with a specific, or "standard," action. This is described more precisely in the text.) Since…
Circle actions on simply connected 4-manifolds
- Mathematics
- 1977
Locally smooth S'-actions on simply connected 4-manifolds are studied in terms of their weighted orbit spaces. An equivariant classification theorem is proved, and the weighted orbit space is used to…
An Orlik–Raymond type classification of simply connected 6-dimensional torus manifolds with vanishing odd-degree cohomology
- Mathematics
- 2016
The aim of this paper is to classify simply connected 6-dimensional torus manifolds with vanishing odd degree cohomology. It is shown that there is a one-to-one correspondence between equivariant…
Circle action with prescribed number of fixed points
- Mathematics
- 2015
Given any two positive integers k and n, this paper is concerned with the existence of a circle action on a closed, smooth orientable n-dimensional manifold with precisely k isolated fixed points. We…
Centered complexity one Hamiltonian torus actions
- Mathematics
- 1999
We consider symplectic manifolds with Hamiltonian torus actions which are “almost but not quite completely integrable”: the dimension of the torus is one less than half the dimension of the manifold.…
Topological toric manifolds
- Mathematics
- 2010
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…