Stanley Casson: 1889–1944

Bing Topology & Casson Handles

In 1914, the 1-dimensional case of the conjecture was proven in full generality by Caratheodory and Osgood-Taylor using elaborate methods from complex analysis. The 2-dimensional case was studied in the 1920s by Alexander who first circulated a manuscript claiming a proof but soon discovered a counterexample himself, the famous horned sphere. Later Alexander found an extra condition under which...

On the Casson Knot Invariant

In our previous paper 19] we introduced a new type of combinatorial formulas for Vassiliev knot invariants and presented lots of formulas of this type. To the best of our knowledge, these formulas are by far the simplest and the most practical for computational purposes. Since then Goussarov has proved the main conjecture formulated in 19]: any Vassiliev knot invariant can be described by such ...

Discriminants of Casson-Gordon invariants

On the Generalized Casson Invariant

The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables is introduced that may allow for more effective invariants. Finally it is shown how the dimensional reduction of these theories corresponds to a generalization of the topologica...

Using Stanley Cavell