Vol. 86, No. 2, 1980

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Recursion formulas for the homology of Ω(X Y )

Giora Dula and Elyahu Katz

Vol. 86 (1980), No. 2, 451–461

A recursion formula for H(Ω(X Y )), the homology of the loop space of the wedge of the spaces X and Y is established when ΩX and ΩY are connected, and have finite dimensional homology. The recursion formula is expressed in terms of HX) and HY ), and applies to dimensions higher than a fixed integer which depends on the dimension of the highest nonvanishing homologies of ΩX and ΩY . A similar but much simpler recursion formula for HX) HY ), the co-product of the two algebras HX) and HY ) is also formulated. If G1 and G2 are topological groups and G1 G2 is their co-product in the category, then our results definitely hold for H(G1 G2) by replacing ΩX by G1, ΩY by G2, and Ω(X Y ) by G1 G2.

Mathematical Subject Classification 2000
Primary: 57T99
Secondary: 55P35
Received: 21 January 1978
Published: 1 February 1980
Giora Dula
Netanya College
42365 Netanya
Elyahu Katz