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Results tagged with examples
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user 1463
For questions requesting examples of a certain structure or phenomenon
8
votes
Applications of logic to group theory?
In recent years, surely the most important and influential (and, unfortunately, sometimes controversial) work on the first-order theory of groups has been Sela's work on free and hyperbolic groups, an …
- 25.2k
8
votes
What can you do with a compact moduli space?
Thurston's compactification of Teichmueller space gives an elegant proof of the Nielsen--Thurston classification of surface automorphisms. The compactified Teichmueller space of the surface of genus …
- 25.2k
17
votes
Applications of the notion of of Gromov-Hausdorff distance
Examples include:
Bestvina's construction of a boundary for the set of hyperbolic structures on a manifold;
Paulin's Theorem: if $\Gamma$ is word-hyperbolic and $\mathrm{Out}(\Gamma)$ is infinite then …
11
votes
Torsion-free virtually free-by-cyclic groups
Many more examples, including ones where the free kernel is finitely generated, arise by looking at knot complements. …
- 25.2k
11
votes
Examples of residually-finite groups
Martino--Minasyan used this construction to give examples of conjugacy separable finitely presented groups with non-conjugacy separable subgroups of finite index. …
37
votes
What are your favorite instructional counterexamples?
The Baumslag--Solitar groups have presentations
$BS(p,q)=\langle a,b\mid a^p=b^{-1}a^q b\rangle$.
They have the following nice properties:
they're two generator, one relator groups;
they can be wr …