2024/02/29 by Marengon, Marco, McDonald, Clayton
#57K10 (Primary) #57K40 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2403.00057
We show that there exists a link with 2 components which is not smoothly slice in \mathbbCP2 # \mathbbCP2. By contrast, it is well-known that every knot (i.e., link with 1 component) is smoothly slice therein. Our proof uses classical topological and smooth obstructions, as well as constructive arguments to exploit the symmetries of the problem. As a consequence, we show that there are infinitely many integer homology 3-spheres such that if any of them bounds a ribbon integer homology 4-ball, than there exists an exotic \mathbbCP2 # \mathbbCP2.