# 3d manifolds ## Refs - triangulation theorem - [[1952#Moise]] - Heegaard splitting - Heegaard 1916: original - [[2000#Scharlemann]] - [[1988#Moriah]]: Seifert - [[1995#Schultens]]: Seifert with boundary ## Links and - Lickorish: every closed, connected, orientable, 3-manifold is obtainable from $S^3$ by removing a finite number of solid tori and sewing them back. (Each solid torus can be thought of as the tubular neighbourhood of a closed knot.) ## Hyperbolic manifold Hyperbolic 3-manifolds are ones that admit an on-shell metric (constant negative curvature). They have finite order bulk mapping class groups. The mapping class group for such a manifold is generated by the isometries of the on-shell metric. ## Heegaard splitting Every closed, orientable three-manifold can be divided into two handlebodies by Heegaard splitting. Every three-manifold with boundaries can be partitioned into two compression bodies via the so-called generalised Heegaard splitting.