Floer homology and knot complements
Jacob Rasmussen
Abstract
We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CFr. It carries information about the Floer homology of large integral surgeries on the knot. Using the exact triangle, we derive information about other surgeries on knots, and about the maps on Floer homology induced by certain surgery cobordisms. We define a certain class of perfect knots in S3 for which CFr has a particularly simple form. For these knots, formal properties of the Ozsvath-Szabo theory enable us to make a complete calculation of the Floer homology. This is the author's thesis; many of the results have been independently discovered by Ozsvath and Szabo in math.GT/0209056.
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