This article describes a software named KnotPortal for visualization of branched covers knots based on an idea by Bill Thurston to view knot as portal other universes. Our implementation allows users explore these knotted portals either screen or in virtual reality using head-mounted device with room-tracking. not only see glued different worlds, but experience them being able walk through the ...

Given a double cover between 3-manifolds branched along nullhomologous link, we establish an inequality the dimensions of their Heegaard Floer homologies. We discuss relationship with L-space conjecture and give some other topological applications, as well analogous result for sutured homology.