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The MOD 2 K-Homology of Ω3 S 3 X

Published online by Cambridge University Press:  20 November 2018

J. G. Mayorquin
J. G. Mayorquin*
Affiliation:
Memorial University, St. John's, Newfoundland
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In order to compute the group K *(Ω3 S 3 X; Z/2) when X is a finite, torsion free CW-complex we apply the techniques developed by Snaith in [38], [39], [40], [41] which were used in [42] to determine the Atiyah-Hirzebruch spectral sequence ( [11], [1, Part III])

for X as above. Roughly speaking the method consists in defining certain classes in K *(Ω3 S 3 X; Z/2) via the π-equivariant mod 2 K-homology of S 2 × Y 2,

([35]), π the cyclic group of order 2 (acting antipodally on S 2, by permuting factors in Y 2, and diagonally on S 2 × Y 2), Y a finite subcomplex of Ω3 S 3 X, and then showing that the classes so produced map under the edge homomorphism to cycles (in the E 1-term of the Atiyah-Hirzebruch spectral sequence for

which determine certain homology classes of H *(Ω3 S 3 X; Z/2), thus exhibiting these as infinite cycles of the spectral sequence

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 1 , 01 February 1988 , pp. 142 - 196
Copyright
Copyright © Canadian Mathematical Society 1988

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