Mathematics Colloquia and Seminars

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First of all, we will see one of the classical invariants in Knot theory. Let K be a knot in S^3. A surface F in S^3 is called a spanning surface or Seifert surface of K if F is orientable and the boundary of F, partial F, is K. We define the genus of K, g(K), by min {genus (F)| partial F= K, and F orientable}.

The existence of such a surface was settled by Seifert using a mechanical method which is named after him as Seifert's Algorithm.

We will see the definition of Seifert's algorithm and some celebrated theorems along with mystery about this algorithm. Then we will see recent developments in this area. If time allows, I would like to go over technical examples.