L-space
In mathematics , L-spaces are certain 3-manifolds whose Heegaard-Floer homology is the simplest possible. The L-space conjecture suggests a connection with the (non) arrangability of fundamental groups and the (non) existence of tight foliage.
definition
A closed, orientable 3-manifold is an L-space if it is a rational sphere of homology and its Heegaard-Floer homology is a free Abelian group with generators.
Examples
Spherical 3-manifolds are L-spaces, this is especially the case for lens spaces . Also coherent sums of spherical 3-manifolds are L-spaces.
L-space conjecture
The L-space conjecture says that the following conditions should be equivalent for irreducible rational homology spheres:
- is not an L-space,
- the fundamental group is an ordered group ,
- has tight foliage .
literature
- Boyer- Gordon- Watson: On L-spaces and left-orderable fundamental groups , Math. Ann. 356: 1213-1245 (2013).