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AbstractIn this paper we study non-negatively curved and rationally elliptic GKM$$_4$$ 4 manifolds and orbifolds. We show that their rational cohomology rings are isomorphic to the rational cohomology of certain model orbifolds. These models are quotients of isometric actions of finite groups on non-negatively curved torus orbifolds. Moreover, we give a simplified proof of a characterisation of products of simplices among orbit spaces of locally standard torus manifolds. This characterisation was originally proved in Wiemeler (J Lond Math Soc 91(3): 667–692, 2015) and was used there to obtain a classification of non-negatively curved torus manifolds.

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The cohomology rings of the orbit spaces of free transformation groups of the product of two spheres

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-00-05668-9 ◽

2000 ◽

Vol 129 (3) ◽

pp. 921-930 ◽

Cited By ~ 8

Author(s):

Ronald M. Dotzel ◽

Tej B. Singh ◽

Satya P. Tripathi

Keyword(s):

Transformation Groups ◽

Orbit Spaces ◽

Cohomology Rings

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THE COHOMOLOGY RING OF ORBIT SPACES OF FREE -ACTIONS ON SOME DOLD MANIFOLDS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972717001058 ◽

2018 ◽

Vol 97 (2) ◽

pp. 340-348

Author(s):

ANA MARIA M. MORITA ◽

DENISE DE MATTOS ◽

PEDRO L. Q. PERGHER

Keyword(s):

Fixed Point ◽

Natural Number ◽

Cohomology Ring ◽

Orbit Spaces ◽

Cohomology Rings ◽

Free Actions

We determine the possible $\mathbb{Z}_{2}$-cohomology rings of orbit spaces of free actions of $\mathbb{Z}_{2}$ (or fixed point free involutions) on the Dold manifold $P(1,n)$, where $n$ is an odd natural number.

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The Torsion versus the Cohomology Rings

Torsions of 3-dimensional Manifolds ◽

10.1007/978-3-0348-7999-6_3 ◽

2002 ◽

pp. 31-51

Author(s):

Vladimir Turaev

Keyword(s):

Cohomology Rings

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Cohomology of groups and splendid equivalences of derived categories

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410100545x ◽

2001 ◽

Vol 131 (3) ◽

pp. 459-472 ◽

Cited By ~ 1

Author(s):

ALEXANDER ZIMMERMANN

Keyword(s):

Group Ring ◽

Local Structure ◽

Cohomology Ring ◽

Derived Categories ◽

Derived Category ◽

Restriction Map ◽

Group Rings ◽

Cohomology Rings ◽

The Impact ◽

Cohomology Of Groups

In an earlier paper we studied the impact of equivalences between derived categories of group rings on their cohomology rings. Especially the group of auto-equivalences TrPic(RG) of the derived category of a group ring RG as introduced by Raphaël Rouquier and the author defines an action on the cohomology ring of this group. We study this action with respect to the restriction map, transfer, conjugation and the local structure of the group G.

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