March 2017 April 2017 May 2017
Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa
123 4 1 1 2 3 4 5 6
5 6789 10 11 2 34567 8 7 8 9 10 11 12 13
12 13 14 15 16 17 18 9 10 111213 14 15 14 15 16 17 18 19 20
19 2021222324 25 16 17181920 21 22 21 22 23 24 25 26 27
26 27282930 31 23 24 25 26 27 28 29 28 29 30 31
30
2:30 pm Tuesday, April 11, 2017 Thesis Defense: Derivatives of genus one and three knots
by JungHwan Park, Ph.D. Candidate (Rice University) in Sewall Hall, Rm. 301
A derivative L of an algebraically slice knot K is an oriented link disjointly embedded in a Seifert surface of K such that its homology class forms a basis for a metabolizer H of K. For genus one knots, we produce a new example of a smoothly slice knot with non-slice derivatives. Such examples were first discovered by Cochran and Davis. In order to do so, we define an operation on a homology B4 that we call an n-twist annulus modification. Further, we give a new construction of smoothly slice knots and exotically slice knots via n-twist annulus modifications. For genus three knots, we show that the set SK,H = {µ¯L(123) − µ¯LI (123) | L, LI ∈ dK/dH} contains n · Z, where dK/dH is the set of all the derivatives associated with a metabolizer H and n is an integer determined by a Seifert form of K and a metabolizer H. As a corollary, we show that it is possible to realize any integer as the Milnor’s triple linking number of a derivative of the unknot on a fixed Seifert surface.
Host Department: Rice University-Mathematics Submitted by lpl1@rice.edu