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A MOD TWO ANALOGUE OF A CONJECTURE OF COOKE
Published online by Cambridge University Press: 01 February 1997
Abstract
The mod two cohomology of the three connective covering of S3 has the form
formula here
where x2n is in degree 2n and n = 2. If F denotes the homotopy theoretic fibre of the map S3 → B2S1 of degree 2, then the mod2 cohomology of F is also of the same form for n = 1. Notice (cf. Section 7 of the present paper) that the existence of spaces whose cohomology has this form for high values of n would immediately provide Arf invariant elements in the stable stem. Hence, it is worthwhile to determine for what values of n the above algebra can be realized as the mod2 cohomology of some space. The purpose of this paper is to construct a further example of a space with such a cohomology algebra for n = 4 and to show that no other values of n are admissible. More precisely, we prove the following.
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- Research Article
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- The London Mathematical Society 1997