Cohomology rings of a class of torus manifolds

Non-negatively curved GKM orbifolds

Mathematische Zeitschrift ◽

10.1007/s00209-021-02853-0 ◽

2021 ◽

Author(s):

Oliver Goertsches ◽

Michael Wiemeler

Keyword(s):

Finite Groups ◽

Orbit Spaces ◽

Cohomology Rings ◽

Negatively Curved ◽

Rational Cohomology ◽

Isometric Actions ◽

Torus Manifolds

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 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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