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math.GT2025
Dehn surgery functions are never injective
Kyle Hayden, Lisa Piccirillo, Laura Wakelin
We prove that, for each fixed rational number , there exists a pair of distinct knots whose -surgeries are orientation-preservingly homeomorphic. This conf…
math.GT2025
Distinguishing closed 4-manifolds by slicing
Tye Lidman, Lisa Piccirillo
One approach to produce a pair of homeomorphic-but-not-diffeomophic closed 4-manifolds is to find a knot which is smoothly slice in one but not the other. This approach has never b…
math.GT2025
Stably irreducible non-orientable knotted surfaces
Tye Lidman, Lisa Piccirillo
We give an elementary obstruction to reducibility for knotted surfaces in the four-sphere. As a new application, we construct stably irreducible non-orientable surfaces.