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Three-Dimensional Manifolds, Skew-Gorenstein Rings and their Cohomology.
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)Report (Other academic)
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 first 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
2010. , 21 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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Research subject
URN: urn:nbn:se:su:diva-35080OAI: diva2:286356
Available from: 2011-01-25 Created: 2010-01-14 Last updated: 2011-01-25Bibliographically approved

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Roos, Jan-Erik
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Department of Mathematics

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