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THE ${ \mathbb{F} }_{2} $-COHOMOLOGY RINGS OF $ \mathbb{S} {\text{ol} }^{3} $-MANIFOLDS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  27 September 2013

J. A. HILLMAN
J. A. HILLMAN*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
*
jonathan.hillman@sydney.edu.au
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Abstract

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We compute the rings ${H}^{\ast } (N; { \mathbb{F} }_{2} )$ for $N$ a closed $ \mathbb{S} {\mathrm{ol} }^{3} $-manifold, and then determine the Borsuk–Ulam indices $\text{BU} (N, \phi )$ with $\phi \not = 0$ in ${H}^{1} (N; { \mathbb{F} }_{2} )$.

Keywords

Borsuk–Ulam theoremcohomology𝕊ol3-manifold

MSC classification

Secondary: 57M99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 191 - 201
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Bauval, A., Gonçalves, D. L., Hayat, C. and Zvengrowski, P., ‘The Borsuk–Ulam Theorem for double coverings of Seifert manifolds’, Proc. Brazilian-Polish Topology meeting, July 2012, Proc. Inst. Math. Natl. Akad. Sci. Ukraine, to appear.Google Scholar
Carlson, J. F., ‘Cohomology of 2-groups’, www.math.uga.edu/~jfs/groups2/cohomology2.html.Google Scholar
Gonçalves, D. L., Hayat, C. and Zvengrowski, P., ‘The Borsuk–Ulam theorem for manifolds, with applications to dimensions two and three’, in Group Actions and Homogeneous Spaces, Fak. Mat. Fyziky Inform. Univ. Komenského, Bratislava (2010), 9–28.Google Scholar
Hillman, J. A., ‘The kernel of integral cup product’, J. Aust. Math. Soc. 43 (1987), 10–15.CrossRefGoogle Scholar
Hillman, J. A., Four-Manifolds, Geometries and Knots, GT Monographs, 5 (Geometry and Topology Publications, 2002); latest revision: see http://www.maths.usyd.edu.au/u/jonh/.Google Scholar
Martins, S. T., Aproximações da diagonal e anéis da cohomologia dos grupos fundamentales das superfícies, de fibrados do toro e de certos grupos virtualmente cíclicos, PhD Thesis, Universidade de São Paulo, 2012.Google Scholar
J. Matoušek (with A. Björner and G. M. Ziegler). Using the Borsuk–Ulam Theorem, Lectures on Topological Methods in Combinatorics and Geometry (Universitext, Springer, Berlin, 2003).Google Scholar
Robinson, D. J. S., A Course in the Theory of Groups, Graduate Texts in Mathematics, 80 (Springer, New York, 1982).CrossRefGoogle Scholar