Volume 19, 1983
ON WEAKLY ALMOST COMPLEX MANIFOLDS WITH
VANISHING DECOMPOSABLE CHERN NUMBERS.
We describe the subgroup of the complex bordism ring consisting of
elements with only the indecomposable Chern monomial giving a non-
zero Chern number. In dimensions 4k
2 we recover results of Ray,
and in dimensions 4k we prove a conjecture of Dyer.
In this note we will investigate the subgroup of the complex bordism
ring MU* consisting of classes for which the only non-zero Chern number is
that coming from the top diMensional Chern class. In dimensions of fom
2, we recover results of [Ra]; in dimensions of form 4k, we prove an
old conjecture of E. Dyer [Dy].
Theorem Let Xn
MU 2n be in the subgroup of eleMents for which all
decomposable Chern numbers are zero. Then Xn is a generator if and only
if cn(Xn) takes the value (up to sign)
2, if n
(2k)!, if n 2k
1, k 1,
dk(2k- 1)!, if n
is the denominator of
B2k/2k, for B 2k the 2k-th Bernoulli number.
1980 Mathematics Subject Classification. 55R50, 57R77
1983 American Mathematical Society
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