4 papers
Spaces of Knots
Allen Hatcher
We consider the space of all smooth knots in the 3-sphere isotopic to a given knot, with the aim of finding a small subspace onto which this large space deformation retracts. For t…
Pants Decompositions of Surfaces
Allen Hatcher
We consider collections of disjoint simple closed curves in a compact orientable surface which decompose the surface into pairs of pants. The isotopy classes of such curve systems…
Spaces of Incompressible Surfaces
Allen Hatcher
This is a "software upgrade" to a paper originally published in 1976, with cleaner statements and improved proofs. The main result is that, in a Haken 3-manifold, the space of all…
Bianchi Orbifolds of Small Discriminant
Allen Hatcher
This brief report (6 pages) was written in 1983 but never published. It concerns the hyperbolic 3-orbifolds obtained as quotients of hyperbolic 3-space by the group of invertible 2…