Spheres not admitting smooth odd-fixed-point actions of \(S_5\) and \(SL(2, 5)\)

zbMath1439.57056MaRDI QIDQ2176711

Shunsuke Tamura, Masaharu Morimoto

Publication date: 5 May 2020

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1579079107

zbMATH Keywords

effective actionhomology sphereone fixed-point action

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Finite groups of transformations in algebraic topology (including Smith theory) (55M35)

Related Items

Appendix to P. Mizerka's theorem ⋮ Exclusions of smooth actions on spheres of the non-split extension of \(C_2\) by \(\mathrm{SL}(2,5)\) ⋮ Construction of one-fixed-point actions on spheres of nonsolvable groups. I ⋮ REMARKS ON DIMENSION OF HOMOLOGY SPHERES WITH ODD NUMBERS OF FIXED POINTS OF FINITE GROUP ACTIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On one fixed point actions on spheres
• Transformation groups
• One fixed point actions on spheres. I,II
• One fixed point actions on low-dimensional spheres
• Fixed-point sets of group actions on finite acyclic complexes
• Surgery on products with finite fundamental group
• \(S^ 4\) does not have one fixed point actions
• Most standard spheres have smooth one fixed point actions of \(A_ 5\). II
• The fixed point set of a finite group action on a homotopy four sphere
• A remark on a fixed point of finite group action on \(S^ 4\)
• Smith equivalence and finite Oliver groups with Laitinen number 0 or 1
• Transformations of finite period
• Fiberings with singularities
• $\mathrm {SL}(2, 5)$ Has no Smooth Effective One-fixed-point Action on $S^8$
• Smith equivalent ${\pmb {{\rm {Aut}}(A_6)}}$-representations are isomorphic
• Pseudofree Representations and 2-Pseudofree Actions on Spheres
• Actions of Groups of Odd Order on Compact, Orientable Manifolds
• Finite groups with smooth one fixed point actions on spheres
• Smith equivalence of representations for finite perfect groups
• Nonexistence of smooth effective one fixed point actions of finite Oliver groups on low-dimensional spheres
• The dimension of spheres with smooth one fixed point actions