The Log-Approximate-Rank Conjecture Is False

2020 ◽  
Vol 67 (4) ◽  
pp. 1-28
Author(s):  
Arkadev Chattopadhyay ◽  
Nikhil S. Mande ◽  
Suhail Sherif
Keyword(s):  
Rank Conjecture

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.

The maximal rank conjecture for non-special curves in ? n

1987 ◽  
Vol 196 (3) ◽  
pp. 355-367 ◽  
Author(s):  
Edoardo Ballico ◽  
Philippe Ellia
Keyword(s):  
Maximal Rank ◽  
Maximal Rank Conjecture ◽  
Rank Conjecture

scholarly journals Min-rank conjecture for log-depth circuits

2011 ◽  
Vol 77 (6) ◽  
pp. 1023-1038 ◽  
Author(s):  
Stasys Jukna ◽  
Georg Schnitger
Keyword(s):  
Rank Conjecture

scholarly journals The co-rank conjecture for 3–manifold groups

2002 ◽  
Vol 2 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Christopher J Leininger ◽  
Alan W Reid
Keyword(s):  
Rank Conjecture
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