Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T01:01:57.722Z Has data issue: false hasContentIssue false
  • English
  • Français

The kernel of integral cup product

Part of: Connections with homological algebra and category theory

Published online by Cambridge University Press:  09 April 2009

Jonathan A. Hillman  and
J. H. Rubinstein
Jonathan A. Hillman
Affiliation:
School of Mathematics and Physics, Macquarie University, North Ryde, NSW, 2113, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We compute the kernel of cup product of 1-dimensional cohomology classes for a group G acting trivially on Z or F2, by means of the naturality of cup product and the 5-term exact sequence of low degree of a suitable LHS spectral sequence. We determine thereby when cup product is injective, and when it is null.

Keywords

cohomologycup productLHS spectral sequence

MSC classification

Secondary: 20J05: Homological methods in group theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 10 - 15
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Dwyer, W. G., ‘Homology, Massey products and maps between groups’, J. Pure Appl. Algebra 6 (1975), 177–190.Google Scholar
[2]Hillman, J. A., ‘The kernel of the cup product’, Bull. Austral. Math. Soc. 32 (1985), 261–274.CrossRefGoogle Scholar
[3]Lambe, L. A., ‘Two exact sequences in rational homotopy theory relating cup products and commutators’, Proc. Amer. Math. Soc. 96 (1986), 360–364.CrossRefGoogle Scholar
[4]Massey, W. S. and Traldi, L., ‘On a conjecture of K. Murasugi’, Pacific J. Math. 124 (1986), 193–213.Google Scholar
[5]Sullivan, D., ‘On the intersection ring of a compact three-manifold’, Topology 14 (1975), 275–277.Google Scholar
[6]Wood, J. C., ‘A theorem on injectivity of the cup product’, Proc. Amer. Math. Soc. 37 (1973), 301–304.CrossRefGoogle Scholar