On the tau invariants in instanton and monopole Floer theories

We unify two existing approaches to the tau invariants in instanton and monopole Floer theories, by identifying , defined by the second author via the minus flavors and of the knot homologies, with , defined by Baldwin and Sivek via cobordism maps of the 3‐manifold homologies induced by knot surgeries. We exhibit several consequences, including a relationship with Heegaard Floer theory, and use our result to compute and for twist knots.