Commuting elements and spaces of homomorphisms
By A. Adem, Frederick R. Cohen. 2006
51 citations recorded by the source corpus.
This article records basic topological, as well as homological properties of the space of homomorphisms Hom(π,G) where π is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If π is a free abelian group of rank equal to n, then Hom(π, G) is the space of ordered n–tuples of commuting elements in G. If G = SU(2), a complete calculation of the cohomology of these spaces is given for n = 2, 3. An explicit stable splitting of these spaces is also obtained, as a special case of a more general splitting.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5134cbdeecf2805f9877c0b1d83290cc3307725d
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Cohomology of the space of commuting n-tuples in a compact Lie group (2006, background): “] and [KS], particularly when n= 3. One striking result to emerge is that Y/G need not be connected, even when Gis simply connected. The study of the nonreduced space Y was initiated more recently in [AC]. There, a scheme for computing integral homology of Y is explained, and carried out in a few ex”