Journal ArticleDOI
Rational cohomology of nilpotent groups and lie algebras
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This article is published in Communications in Algebra.The article was published on 1978-01-01. It has received 43 citations till now. The article focuses on the topics: Nilpotent group & Central series.read more
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Excision in algebraic $K$-theory
Andrei Suslin,Mariusz Wodzicki +1 more
Abstract: Introduction 1. Excision and the homology of affine groups 2. Volodin's spaces 3. Excision for rings with the Triple Factorization Property 4. Lie analogue of Volodin's construction 5. The homology of nilpotent groups and nilpotent Lie algebras 6. A proof of the main theorems 7. The tensor product of H-unital algebras 8. The matrix ring of a small category 9. The acyclicity of triangular complexes 10. A proof of Karoubi's Conjecture
Journal ArticleDOI
Links, pictures and the homology of nilpotent groups
Kiyoshi Igusa,Kent E. Orr +1 more
TL;DR: In this article, a geometric slice-like characterization for the vanishing of Milnor's link invariants was given by proving the k-slice conjecture, which states that a link has vanishing Milnor -invariants of length 2k if and only if bounds disjoint surfaces in a four disk in such a way that the fundamental group of the complement admits free nilpotent quotients of class k.
Journal ArticleDOI
Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant
TL;DR: In this paper, the authors studied the "infinitesimal" version of the k-th Morita homomorphism, which corresponds to the original version by a canonical isomorphism.
Journal ArticleDOI
Cohomology of nilpotent groups of class 2
TL;DR: In this paper, the cohomology rings of a number of nilpotent groups of class 2 for appropriate coefficients are computed for a given set of coefficients, and the basic tool is a suitable small free resolution.
Book ChapterDOI
From mapping class groups to monoids of homology cobordisms: a survey
Kazuo Habiro,Gwenael Massuyeau +1 more
TL;DR: In this paper, the authors survey recent works on the structure of the monoid of homology cobordisms, and outline their relations with the study of the mapping class group.
References
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Journal ArticleDOI
On the Cohomology of Compact Homogeneous Spaces of Nilpotent Lie Groups
TL;DR: In this paper, it was shown that the theory of invariant integrals does not hold for compact homogeneous spaces of non-compact Lie groups and that the cohomology of a homogeneous space of a compact Lie group can be obtained from the complex of invariants on it.
Journal ArticleDOI
The Group Ring Of a Class Of Infinite Nilpotent Groups
TL;DR: In this article, the authors studied the discrete group ring Γ of a finitely generated torsion free nilpotent group over a field of characteristic zero and showed that if Δ is the ideal of Γ spanned by all elements of the form G − 1, where G ∈, then and the only element belonging to Δw for all w is the zero element.