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Three-dimensional Manifolds, Skew-Gorenstein Rings and their Cohomology
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)In: Journal of Commutative Algebra, ISSN 1939-0807, Vol. 2, no 4, 21 p.473-499 p.Article in journal (Refereed) Published
Abstract [en]

Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra). We present some applications of the homological theory of these graded skew-commutative rings. In particular we find compact oriented 3-manifolds without boundary for which the Hilbert series of the Yoneda Ext-algebra of the cohomology ring of the fundamental group is an explicit transcendental function. This is only possible for large Betti numbers of the 3-manifold (bigger than - or maybe equal to - 11). We give also examples of 3-manifolds where the Ext-algebra of the cohomology ring of the fundamental group is not finitely generated.

Place, publisher, year, edition, pages
Tempe, AZ: Rocky Mountain Mathematics Consortium , 2010. Vol. 2, no 4, 21 p.473-499 p.
Keyword [en]
Three-dimensional manifolds. Fundamental group, Lower central series, Gorenstein rings, Hyperplane arrangement, homotopy Lie algebra, Yoneda Ext-algebra, local ring
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URN: urn:nbn:se:su:diva-35527DOI: 10.1216/JCA-2010-2-4-473OAI: diva2:287457
Available from: 2010-01-18 Created: 2010-01-18 Last updated: 2011-01-13Bibliographically approved

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Roos, Jan-Erik
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