Bypass exact triangles and three-manifold invariants

Abstract: There are many gauge-theoretic invariants of three-manifolds which have been very influential in low-dimensional topology over the course of the past twenty or so years. I’ll try and explain why I think a unifying feature of these theories is the existence of so-called ‘bypass exact triangles’ — and, in particular, the relationship between these and other constructions for three-manifolds-with-torus-boundary. I won’t assume any prior knowledge of three-manifolds or gauge-theoretic invariants: my results are structural and algebraic at heart, and closely connected with wrapped Fukaya categories.