One input method for my SURF project is to take an alternating link
projection, shade regions of the link, and then use the shaded regions
and intersections to create a graph (the kind with nodes and edges). For
example, the program Plink
lets a person draw a link with their mouse. Part of the algorithm is
then to load the drawing and shade regions (while keeping track of
them), like in the picture below.
Link drawn in Plink (left) and shaded regions (right)
Based on the shaded regions and intersections, a graph and quadratic form can be calculated for each link projection. The quadratic form can then be used to calculate the Heegaard Floer correction terms.
Since I’m doing a math SURF, I don’t have to go to a lab or anywhere specific on campus to work on the project. Although the view from my dorm room is very nice, it can get lonely in the morning since most people are at labs or JPL. So for the first day, I decided to go work in Annenberg (the computer science building), since they have an undergraduate computer lab.
View from my summer dorm room (the blurriness is from the window screen)
For some of the other inputing methods for the SURF project, I’ll first have to learn more about
topology and read a little about homology. My list of topics to learn about include plumbed 3-manifolds, Seifert fibered rational
homology spheres, and Dehn surgery. Fortunately I know several other math majors staying at Caltech over the summer!