scholarly journals The Hopf conjecture for positively curved manifolds with discrete abelian group actions

2008 ◽  
Vol 26 (3) ◽  
pp. 313-322 ◽  
Author(s):  
Xiaole Su ◽  
Yusheng Wang
Keyword(s):  
Abelian Group ◽  
Group Actions ◽  
Curved Manifolds ◽  
Hopf Conjecture ◽  
Abelian Group Actions ◽  
Positively Curved ◽  
Discrete Abelian Group

THE HOPF CONJECTURE FOR MANIFOLDS WITH ABELIAN GROUP ACTIONS

2005 ◽  
Vol 07 (01) ◽  
pp. 121-136 ◽  
Author(s):  
XIAOCHUN RONG ◽  
XIAOLE SU
Keyword(s):  
Fixed Point ◽  
Abelian Group ◽  
Sectional Curvature ◽  
Euler Characteristic ◽  
Group Actions ◽  
Closed Manifold ◽  
Positive Sectional Curvature ◽  
Hopf Conjecture ◽  
Abelian Group Actions

Let M be a closed even n-manifold of positive sectional curvature on which a torus Tk acts isometrically. We show that if [Formula: see text] (respectively, k > 1) for n ≠ 12 (respectively, n = 12), then the Euler characteristic of each Tk-fixed point component is positive. This implies that the Euler characteristic of M is positive. We also extend this result to an isometric elementary p-group [Formula: see text]-action on a closed manifold of positive sectional curvature.

scholarly journals On abelian group actions with TNI-centralizers

2019 ◽  
Vol 47 (7) ◽  
pp. 3003-3006
Author(s):  
Gülin Ercan ◽  
İsmail Ş. Güloğlu
Keyword(s):  
Abelian Group ◽  
Group Actions ◽  
Abelian Group Actions

scholarly journals Local Weyl modules for equivariant map algebras with free abelian group actions

2012 ◽  
Vol 350 (1) ◽  
pp. 386-404 ◽  
Author(s):  
Ghislain Fourier ◽  
Tanusree Khandai ◽  
Deniz Kus ◽  
Alistair Savage
Keyword(s):  
Abelian Group ◽  
Free Abelian Group ◽  
Group Actions ◽  
Weyl Modules ◽  
Equivariant Map ◽  
Abelian Group Actions
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