Nonexistence of smooth effective one fixed point action of finite Oliver groups on low-dimensional spheres

• Autorzy: Borowiecka A. , Mizerka P.

Identyfikatory

DOI

10.4064/ba8150-9-2018

• Języki publikacji: EN

Abstrakty

EN

According to Laitinen and Morimoto (1998), a finite group G has a smooth effective one fixed point action on some sphere if and only if G is an Oliver group. For some finite Oliver groups G of order up to 216, and for G = A₅ x C_p, where p = 3, 5, 7, we present a strategy of excluding smooth effective one fixed point G-actions on low-dimensional spheres.

Słowa kluczowe

EN

intersection number; smooth-effective one-fixed point actions on spheres

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2018
• Tom: Vol. 66, no. 2
• Strony: 167--177
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Borowiecka A.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland

autor

Mizerka P.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland

Bibliografia

• [1] M. Audin, Torus Actions on Symplectic Manifolds, rev. ed., Progr. Math. 93, Birkhäuser, Basel, 2004.
• [2] A. Borowiecka, SL(2, 5) has no smooth effective one-fixed-point action on S8, Bull. Polish Acad. Sci. Math. 64 (2016), 85-94.
• [3] G. E. Bredon, Introduction to Compact Transformation Groups, Pure Appl. Math. 46, Academic Press, New York, 1972.
• [4] N. P. Buchdahl, S. Kwasik and R. Schultz, One fixed point actions on low-dimensional spheres, Invent. Math. 102 (1990), 633-662.
• [5] J. F. Davis and P. Kirk, Lecture Notes in Algebraic Topology, Grad. Stud. Math. 35, Amer. Math. Soc., Providence, RI, 2001.
• [6] M. Furuta, A remark on a fixed point of finite group action on S4, Topology 28 (1989), 35-38.
• [7] The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.8.10, 2018.
• [8] E. Laitinen and M. Morimoto, Finite groups with smooth one fixed point actions on spheres, Forum Math. 10 (1998), 479-520.
• [9] E. Laitinen, M. Morimoto and K. Pawałowski, Deleting-inserting theorem for smooth actions of finite nonsolvable groups on spheres, Comment. Math. Helv. 70 (1995), 10-38.
• [10] M. Morimoto, On one fixed point actions on spheres, Proc. Japan Acad. Ser. A Math. Sci. 63 (1987), 95-97.
• [11] B. Oliver, Fixed point sets and tangent bundles of actions on disks and Euclidean spaces, Topology 35 (1996), 583-615.
• [12] E. Stein, Surgery on products with finite fundamental group, Topology 16 (1977), 473-493.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).