Over the last 20 years, the Rasmussen invariant of knots in S^3 has had a number of interesting applications to questions about surfaces in B^4. In this talk I will survey some recent extensions of the invariant to knots in other three-manifolds: in connected sums of S^1 x S^2 (joint work with Marengon, Sarkar, and Willis), in RP^3 (joint work with Willis, and also separate work of Chen), and in a general setting (work by Morrison, Walker and Wedrich; and independently by Ren-Willis). I will describe how these invariants give bounds on the genus of smooth surfaces in 4-manifolds, and can even detect exotic 4-manifolds with boundary.

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Meeting ID: 935 6306 2335
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