MATH 7590: Geometric Topology Homework
MATH 7590 Geometric Topology
Some Homework Problems & Potential Presentation Topics
- Under what conditions on a braid is the closure a knot?
- Identify the kernel of the map from the 3-string braid
group B3 to
- Show that the n-string braid group
is generated by the elementary braid sigma1 and
the braid eta =
- Verify that the relations given in class for the pure braid group hold, either
or using the Artin representation (or both).
Potential Presentation Topics
- Study the braid groups of (orientable) surfaces.
E.g., find presentations; discuss the Dirac string problem...
- Use the Reidemeister-Schreier rewriting process to obtain a presentation
for the (abstract)
pure braid group from the homomorphism from the (abstract)
full braid group to the symmetric group.
- Write computer programs to implement the Artin representation; the Dehornoy
- Investigate the structure of the fundamental groups of the orbit
configuration spaces FG(C*,n) and
where G is a finite cylic
group and Sn is the symmetric group.
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