Studying surfaces via closed braids

Details Studying surfaces via closed braids Studying surfaces via closed braids

1998-04-06

arxiv.org/abs/math/9804028v1

Jnl Knot Th 7, No.3 (1998), 267-334

Mathematics

Geometric Topology

61 pages

Scientific paper

This is a review article on the Bennequin-Birman-Menasco machinery for studying embedded incompressible surfaces in 3-space via their `braid foliations'. Two cases are investigated: case (1) The surface has non-empty boundary; the boundary is a knot or link which is represented as a closed braid, Case (2) The surface is closed, but it lies in the complement of a knot or link which is represented as a closed braid. The main results in the area are established with full proofs, in a systematic fashion, with an eye toward making them accessible to the beginning reader. There are some new contributions, described in detail in the introduction.

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