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Symmetric unions without cosmetic crossing changes
Student-Run Geometry/Topology Seminar| Speaker: | Allison Moore, UC Davis |
| Location: | 1147 MSB |
| Start time: | Wed, Sep 28 2016, 2:10PM |
A classic problem in knot theory is the cosmetic crossing conjecture. This conjecture asserts that a crossing change will always change the knot type, unless the crossing is nugatory. In the main geometry seminar I'll describe an obstruction to so-called "cosmetic" crossing changes. In the student seminar, I'll show how to use that obstruction to produce new infinite families of knots for which the conjecture is true. In the process, we'll review branched double covers, L-spaces, and discuss some computational techniques which arise in various homology theories.