1998/04/06 by Joan S. Birman, Elizabeth Finkelstein
Mathematics · #math.GT #msc:57M25 #msc:57M50
published as Jnl Knot Th 7, No.3 (1998), 267-334 · 61 pages
arxiv created 1998/04/06 · arxiv updated 2009/11/30
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.