Vol. 42, No. 1, 1972

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A note on H-equivalences

Donald William Kahn

Vol. 42 (1972), No. 1, 77–80

If X is a space, with base point, the set of homotopy classes of based self-equivalent maps, from X to itself, forms a group, which has been studied by many authors. In this note, we study a related group, in the case where X is an H-space. The main result is that all such groups are finitelypresented. The methods combine results from algebraic topology with combinatorial group theory.

Mathematical Subject Classification
Primary: 55D10
Secondary: 55E05
Received: 5 February 1971
Revised: 24 June 1971
Published: 1 July 1972
Donald William Kahn