scholarly journals Weights, Weyl-Equivariant Maps and a Rank Conjecture

2020 ◽  
pp. 1-4
Author(s):  
Joseph Malkoun
Keyword(s):  
Equivariant Maps ◽  
Rank Conjecture

scholarly journals Stratifications of equivariant varieties

1977 ◽  
Vol 16 (2) ◽  
pp. 279-295 ◽  
Author(s):  
M.J. Field
Keyword(s):  
Lie Group ◽  
General Position ◽  
Higher Order ◽  
Order Conditions ◽  
Compact Lie Group ◽  
Algebraic Varieties ◽  
Equivariant Maps

Let G be a compact Lie group and V and W be linear G spaces. A study is made of the canonical stratification of some algebraic varieties that arise naturally in the theory of C∞ equivariant maps from V to W. The main corollary of our results is the equivalence of Bierstone's concept of “equivariant general position” with our own of “G transversal”. The paper concludes with a description of Bierstone's higher order conditions for equivariant maps in the framework of equisingularity sequences.

Torus actions, maximality, and non-negative curvature

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Escher ◽  
Catherine Searle
Keyword(s):  
Negative Curvature ◽  
Torus Action ◽  
Maximal Symmetry ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Product Of Spheres ◽  
Rank Conjecture ◽  
Simply Connected ◽  
Symmetry Rank ◽  
Special Case

Abstract Let ℳ 0 n {\mathcal{M}_{0}^{n}} be the class of closed, simply connected, non-negatively curved Riemannian n-manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} , then M is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to 3. As a special case, we then prove the Maximal Symmetry Rank Conjecture for all M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} . Finally, we show the Maximal Symmetry Rank Conjecture for simply connected, non-negatively curved manifolds holds for dimensions less than or equal to 9 without additional assumptions on the torus action.

scholarly journals Bourgin–Yang version of the Borsuk–Ulam theorem for ℤpk–equivariant maps

2012 ◽  
Vol 12 (4) ◽  
pp. 2245-2258 ◽  
Author(s):  
Wacław Marzantowicz ◽  
Denise de Mattos ◽  
Edivaldo dos Santos
Keyword(s):  
Equivariant Maps ◽  
Ulam Theorem

Essential Equivariant Maps and Borsuk-Ulam Theorems

2000 ◽  
Vol 61 (3) ◽  
pp. 950-960 ◽  
Author(s):  
Mónica Clapp ◽  
Wacław Marzantowicz
Keyword(s):  
Equivariant Maps

On the Equivariant Formality of Kähler Manifolds With Finite Group Action

1993 ◽  
Vol 45 (6) ◽  
pp. 1200-1210 ◽  
Author(s):  
Benjamin L. Fine ◽  
Georgia Triantafillou
Keyword(s):  
Finite Group ◽  
Group Action ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Maps ◽  
Finite Group Action ◽  
Equivariant Maps ◽  
Definition Of ◽  
A Finite Group

AbstractAn appropriate definition of equivariant formality for spaces equipped with the action of a finite group G, and for equivariant maps between such spaces, is given. Kahler manifolds with holomorphic G-actions, and equivariant holomorphic maps between such Kàhler manifolds, are proven to be equivariantly formal, generalizing results of Deligne, Griffiths, Morgan, and Sullivan

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