紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2023, 60(1), p. 1-14

EXCLUSIONS OF SMOOTH ACTIONS ON SPHERES OF THE NON-SPLIT EXTENSION OF C₂ BY SL(2, 5)

Mizerka, Piotr

Osaka University and Osaka Metropolitan University, Departments of Mathematics

英語

text

2023-01

There are four groups G fitting into a short exact sequence 1 → SL(2, 5) → G → C₂ → 1, where SL(2, 5) is the special linear group of (2 × 2)-matrices with entries in the field of five elements. Except for the direct product of SL(2, 5) and C₂, there are two other semidirect products of these two groups and just one non-semidirect product SL(2, 5).C₂, considered in this paper. It is known that each finite nonsolvable group can act on spheres with arbitrary positive number of fixed points. Clearly, SL(2, 5).C₂ is a nonsolvable group. Moreover, it turns out that SL(2, 5).C₂ possesses a free representation and as such, can potentially act pseudofreely with nonempty fixed point set on manifolds of arbitrarily large dimension. We prove that SL(2, 5).C₂ cannot act effectively with odd number of fixed points on homology spheres of dimensions less than 14. In the special case of effective one fixed point actions on homology spheres, we are able to exclude 15, 16, and 17 from the dimension of them. Moreover, we prove that 5-pseudofree one fixed point actions of SL(2, 5).C₂ on spheres do not exist.

10.18910/89989

89989

EXCLUSIONS OF SMOOTH ACTIONS ON SPHERES OF THE NON-SPLIT EXTENSION OF C₂ BY SL(2, 5)

Mizerka, Piotr

Osaka University and Osaka Metropolitan University, Departments of Mathematics

英語

2023-01

Osaka Journal of Mathematics

60

1

1

14

https://hdl.handle.net/11094/89989

10.18910/89989

https://doi.org/10.18910/89989