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L-space vs left-orderable L-space Conjecture [Boyer-Gordon-Watson, 2011] M : an irreducible rational homology sphere M is an L-space if and only if π 1 (M ) is not LO L-space A rational homology sphere M is called an L-space if rk HF (M ) = |H 1 (M ; Z)| holds for HF (M ): Heegaard Floer homology. left-orderable group A non-trivial group G is called left-orderable (LO) if ∃ <: a strict total order on G which is left invariant: Left-orderable surgery and L-space surgery K: a knot in 3-sphere S 3doi:10.1142/s0218216515500030 fatcat:bnkmi6bk7bhwvhj4idcfgtzvjm