Title: On adic genus, Postnikov conjugates, and lambda-rings
Author: Donald Yau
MSC: 55P15; 55N15, 55P60, 55S25
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
dyau@math.uiuc.edu
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 for any positive integer $n$, the power series
ring $\bZ \lbrack \lbrack x_1, \ldots , x_n \rbrack \rbrack$ admits
uncountably many pairwise non-isomorphic $\lambda$-ring structures.