L-spaces, taut foliations and fibred hyperbolictwo-bridge links

Key Points

• The research aims to establish the relationship between Dehn surgery on fibred hyperbolic two-bridge links and L-spaces, particularly through the presence of taut foliations.
• Proved conditions under which rational homology spheres are not L-spaces.
• Explored the implications of surgeries on two-bridge links and their connection to taut foliations.
• Utilized properties of knot transformations, specifically two-bridge replacements and Whitehead doubling.
• M is not an L-space if and only if it supports a co-orientable taut foliation.
• All nonmeridional surgeries on knots resulting from two-bridge replacements support co-orientable taut foliations.
• Whitehead doubles of nontrivial knots also exhibit supporting nonmeridional surgeries for taut foliations.