Classical pretzel knots and left orderability

Anh Tran (UT Dallas)

Abstract: Heegaard Floer homology is a package of 3-manifold invariants introduced by Ozsvath and Szabo. Manifolds with minimal Heegaard Floer homology are called L-spaces. The L-space conjecture of Boyer, Gordon and Watson states that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. In this talk, we will discuss this conjecture for 3-manifolds obtained from the classical pretzel knots by Dehn surgeries or by taking cyclic branched covers.