On adic genus, Postnikov conjugates, and lambda-rings

Details On adic genus, Postnikov conjugates, and lambda-rings On adic genus, Postnikov conjugates, and lambda-rings

2001-05-24

arxiv.org/abs/math/0105194v1

Mathematics

Algebraic Topology

16 pages

Scientific paper

Sufficient conditions on a space are given which guarantee that the $K$-theory ring and the ordinary cohomology ring with coefficients over a principal ideal domain are invariants of, respectively, the adic genus and the SNT set. An independent proof of Notbohm's theorem on the classification of the adic genus of $BS^3$ by $KO$-theory $\lambda$-rings is given. An immediate consequence of these results about adic genus is that the power series ring $\mathbf{Z} \lbrack \lbrack x \rbrack \rbrack$ admits uncountably many pairwise non-isomorphic $\lambda$-ring structures.

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