On Semi-Free Finite Group Actions on Homotopy Spheres | Zendy

Kōjun Abe | Zendy

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On Semi-Free Finite Group Actions on Homotopy Spheres

Author(s) -

Kōjun Abe

Publication year - 1975

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195191695

Subject(s) - mathematics , homotopy , homomorphism , group (periodic table) , equivariant map , order (exchange) , finite group , combinatorics , homotopy group , spheres , pure mathematics , algebra over a field , discrete mathematics , physics , astronomy , chemistry , organic chemistry , finance , economics

In this paper, we shall study semi-free finite group actions on homotopy spheres. In [8], M. Sebastiani studied semi-free finite group actions on homotopy spheres with two points as the fixed point set. He showed that the collection of equivariant diffeomorphism classes of these semi-free finite group actions is an abelian group under the equivariant connected sum about a fixed point. By the methods analogous to Kervaire-Milnor [4], he proved that this abelian group is a finite group in the case of cyclic group actions.

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