The genus-g handlebody detection conjecture in the 4-sphere
For each g≥0g\geq 0g≥0, let V0,V1⊂S4V_0,V_1\subset S^4V0,V1⊂S4 be 3-dimensional genus-ggg handlebodies with the same boundary, ∂V0=∂V1\partial V_0=\partial V_1∂V0=∂V1. A simple closed curve in ∂V0\partial V_0∂V0 is…