scholarly journals A finite group acting on a rational homology 3-Sphere with 0-dimensional fixed point set must be Z2

Topology ◽  
1997 ◽  
Vol 36 (2) ◽  
pp. 509-518
Author(s):  
Masako Kobayashi ◽  
Erhard Luft ◽  
Shicheng Wang
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Fixed Point Set ◽  
Rational Homology ◽  
Point Set ◽  
A Finite Group

scholarly journals On the realization of the Gelfand character of a finite group as a twisted trace

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jorge Soto-Andrade ◽  
Maria-Francisca Yáñez-Valdés
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Regular Representation ◽  
Natural Representation ◽  
Fixed Point Set ◽  
Linear Automorphism ◽  
Point Set ◽  
A Finite Group ◽  
The Right ◽  
Complex Characters

Abstract We show that the Gelfand character χ G \chi_{G} of a finite group 𝐺 (i.e. the sum of all irreducible complex characters of 𝐺) may be realized as a “twisted trace” g ↦ Tr ⁡ ( ρ g ∘ T ) g\mapsto\operatorname{Tr}(\rho_{g}\circ T) for a suitable involutive linear automorphism 𝑇 of L 2 ⁢ ( G ) L^{2}(G) , where ( L 2 ⁢ ( G ) , ρ ) (L^{2}(G),\rho) is the right regular representation of 𝐺. Moreover, we prove that, under certain hypotheses, we have T ⁢ ( f ) = f ∘ L T(f)=f\circ L ( f ∈ L 2 ⁢ ( G ) f\in L^{2}(G) ), where 𝐿 is an involutive anti-automorphism of 𝐺. The natural representation 𝜏 of 𝐺 associated to the natural 𝐿-conjugacy action of 𝐺 in the fixed point set Fix G ⁡ ( L ) \operatorname{Fix}_{G}(L) of 𝐿 turns out to be a Gelfand model for 𝐺 in some cases. We show that ( L 2 ⁢ ( Fix G ⁡ ( L ) ) , τ ) (L^{2}(\operatorname{Fix}_{G}(L)),\tau) fails to be a Gelfand model if 𝐺 admits non-trivial central involutions.

scholarly journals Surgeries on periodic links and homology of periodic 3-manifolds

2001 ◽  
Vol 131 (2) ◽  
pp. 295-307 ◽  
Author(s):  
JÓZEF H. PRZYTYCKI ◽  
MAXIM V. SOKOLOV
Keyword(s):  
Fixed Point ◽  
Unexpected Result ◽  
Prime Integer ◽  
Interesting Application ◽  
Fixed Point Set ◽  
Rational Homology ◽  
Similar Theorem ◽  
Similar Criterion ◽  
Point Set ◽  
Framed Link

Fix a prime integer p. We show that a closed orientable 3-manifold M admits an action of Zp with the fixed point set S1 if and only if M can be obtained as the result of surgery on a p-periodic framed link L and Zp acts freely on the components of L. We prove a similar theorem for free Zp-actions. As an interesting application, we prove the following, rather unexpected result: for any M as above and for any odd prime p, H1(M, Zp) ≠ Zp. We also prove a similar criterion of 2-periodicity for rational homology 3-spheres.

scholarly journals Betti numbers of fixed point sets and multiplicities of indecomposable summands

2003 ◽  
Vol 74 (2) ◽  
pp. 165-172
Author(s):  
Semra Öztürk Kaptanoglu
Keyword(s):  
Fixed Point ◽  
Equivariant Cohomology ◽  
Betti Numbers ◽  
Localization Theorem ◽  
Fixed Point Set ◽  
Moore Space ◽  
Even Order ◽  
Point Set ◽  
Characteristic 2 ◽  
A Finite Group

AbstractLet G be a finite group of even order, k be a field of characteristic 2, and M be a finitely generated kG-module. If M is realized by a compact G-Moore space X, then the Betti numbers of the fixed point set XCn and the multiplicities of indecomposable summands of M considered as a kCn-module are related via a localization theorem in equivariant cohomology, where Cn is a cyclic subgroup of G of order n. Explicit formulas are given for n = 2 and n = 4.

scholarly journals Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhao-Rong Kong ◽  
Lu-Chuan Ceng ◽  
Qamrul Hasan Ansari ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Hybrid Extragradient Method ◽  
Point Set ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

Stein manifolds of nonnegative curvature

2018 ◽  
Vol 18 (3) ◽  
pp. 285-287
Author(s):  
Xiaoyang Chen
Keyword(s):  
Fixed Point ◽  
Sectional Curvature ◽  
Normal Bundle ◽  
Stein Manifold ◽  
Riemannian Metric ◽  
Nonnegative Curvature ◽  
Fixed Point Set ◽  
Nonnegative Sectional Curvature ◽  
Point Set ◽  
Nonempty Compact

AbstractLet X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ*g = g.

scholarly journals On soft quasi-pseudometric spaces

2021 ◽  
Vol 22 (1) ◽  
pp. 17
Author(s):  
Hope Sabao ◽  
Olivier Olela Otafudu
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Soft Set ◽  
Fixed Point Set ◽  
Point Set ◽  
The Absolute ◽  
Pseudometric Space

<p>In this article, we introduce the concept of a soft quasi-pseudometric space. We show that every soft quasi-pseudometric induces a compatible quasi-pseudometric on the collection of all soft points of the absolute soft set whenever the parameter set is finite. We then introduce the concept of soft Isbell convexity and show that a self non-expansive map of a soft quasi-metric space has a nonempty soft Isbell convex fixed point set.</p>

scholarly journals Finite groups acting on hyperelliptic 3-manifolds

2020 ◽  
Vol 29 (04) ◽  
pp. 2050021
Author(s):  
Mattia Mecchia
Keyword(s):  
Fixed Point ◽  
Simple Group ◽  
Finite Groups ◽  
Prime Power ◽  
Simple Groups ◽  
Fixed Point Set ◽  
Point Set

We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to [Formula: see text] Such involutions are called hyperelliptic as the manifolds admitting such an action. We consider finite groups acting on 3-manifolds and containing hyperelliptic involutions whose fixed-point set has [Formula: see text] components. In particular we prove that a simple group containing such an involution is isomorphic to [Formula: see text] for some odd prime power [Formula: see text], or to one of four other small simple groups.

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