- Have they published with their students?
- Where have their students ended up after the PhD?
- Get feedback from their previous students
- Work on a project they are interested in
[knot theory] [invariants]
The writhe of an oriented knot is invariant under change of orientation. i.e. the writhe is an invariant of unoriented knots. (NOTE: But it’s not invariant under change of orientation for links!)
Hence the normalized Kauffman bracket polynomial of a knot is invariant under change of orientation.
has characteristic polynomial .
Given an additive category we can form the Grothendieck group . If further is a tensor category then is also a ring, the Grothendieck ring.
If is semisimple then any equality in corresponds to an isomorphism in .
This is a scratchpad for my summer school course in vector bundles and K-theory.
Given local trivializations of a vector bundle on open sets whose intersection is non-empty, these local trivializations define a clutching function (or ), since on the intersection the composite restricted to each is a linear isomorphism.
Given vector bundles , define .
Subgroups of finitely-generated abelian groups are finitely-generated.
Not necessarily true for finitely-generated non-abelian groups.
1. For a polynomial with roots ,