Definition:Seifert Matrix
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Definition
For a knot $K$ with Seifert surface $S$, the Seifert matrix $V$ of $K$ is defined by its entries as:
- $v_{ij} = \operatorname{lk} \left({ x_i, x_k^* }\right)$
where:
- the $x_a$ are the generators of the fundamental group $\pi_1(S)$
- $x_a^*$ is the positive push-off of $x_a$
- $\operatorname{lk}$ is the linking number of the two loops.
Source of Name
This entry was named for Karl Johannes Herbert Seifert.