Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-08T11:26:35.791Z Has data issue: false hasContentIssue false

A MOD TWO ANALOGUE OF A CONJECTURE OF COOKE

Published online by Cambridge University Press:  01 February 1997

J. AGUADÉ
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
C. BROTO
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
D. NOTBOHM
Affiliation:
Mathematisches Institut der Georg August Universität Göttingen, Bunsenstrasse 3, 37073 Göttingen, Germany
Get access

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 S3B2S1 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.

Type
Research Article
Copyright
The London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)