FREE FINITE GROUP ACTIONS ON RATIONAL HOMOLOGY 3-SPHERES

Forum of Mathematics Sigma ◽

10.1017/fms.2019.24 ◽

2019 ◽

Vol 7 ◽

Author(s):

ALEJANDRO ADEM ◽

IAN HAMBLETON

Keyword(s):

Finite Group ◽

Finite Groups ◽

Group Actions ◽

Rational Homology ◽

Finite Group Actions ◽

Rational Homology Spheres ◽

Cohomology Of Groups

We use methods from the cohomology of groups to describe the finite groups which can act freely and homologically trivially on closed 3-manifolds which are rational homology spheres.

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Polarization of Separating Invariants

Canadian Journal of Mathematics ◽

10.4153/cjm-2008-027-2 ◽

2008 ◽

Vol 60 (3) ◽

pp. 556-571 ◽

Cited By ~ 20

Author(s):

Jan Draisma ◽

Gregor Kemper ◽

David Wehlau

Keyword(s):

Finite Group ◽

Finite Groups ◽

Group Actions ◽

Upper Bounds ◽

Weyl’S Theorem ◽

Finite Group Actions ◽

Separating Invariants ◽

The Difference ◽

Special Case

AbstractWe prove a characteristic free version of Weyl’s theorem on polarization. Our result is an exact analogue ofWeyl’s theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of cheap polarization, and show that it is enough to take cheap polarizations of invariants of just one copy of a representation to obtain separating vector invariants for any number of copies. This leads to upper bounds on the number and degrees of separating vector invariants of finite groups.

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Extending finite group actions on surfaces to hyperbolic 3-manifolds

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100072960 ◽

1995 ◽

Vol 117 (1) ◽

pp. 137-151 ◽

Cited By ~ 3

Author(s):

Monique Gradolato ◽

Bruno Zimmermann

Keyword(s):

Finite Group ◽

Riemann Surface ◽

Finite Groups ◽

Group Actions ◽

Geodesic Boundary ◽

Totally Geodesic ◽

Finite Group Actions ◽

Closed Riemann Surface ◽

A Finite Group ◽

The Given

Let G be a finite group of orientation preserving isometrics of a closed orientable hyperbolic 2-manifold Fg of genus g > 1 (or equivalently, a finite group of conformal automorphisms of a closed Riemann surface). We say that the G-action on Fgbounds a hyperbolic 3-manifold M if M is a compact orientable hyperbolic 3-manifold with totally geodesic boundary Fg (as the only boundary component) such that the G-action on Fg extends to a G-action on M by isometrics. Symmetrically we will also say that the 3-manifold M bounds the given G-action. We are especially interested in Hurwitz actions, i.e. finite group actions on surfaces of maximal possible order 84(g — 1); the corresponding finite groups are called Hurwitz groups. First examples of bounding and non-bounding Hurwitz actions were given in [16].

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Crossed products by actions of finite groups with the Rokhlin property

International Journal of Mathematics ◽

10.1142/s0129167x15500421 ◽

2015 ◽

Vol 26 (07) ◽

pp. 1550042 ◽

Cited By ~ 6

Author(s):

Luis Santiago

Keyword(s):

Finite Group ◽

Finite Groups ◽

Group Actions ◽

Crossed Product ◽

Crossed Products ◽

Finite Group Actions ◽

C Algebras ◽

Type Property ◽

The Given

We introduce and study a Rokhlin-type property for actions of finite groups on (not necessarily unital) C*-algebras. We show that the corresponding crossed product C*-algebras can be locally approximated by C*-algebras that are stably isomorphic to closed two-sided ideals of the given algebra. We then use this result to prove that several classes of C*-algebras are closed under crossed products by finite group actions with this Rokhlin property.

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