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Raising crosscap number while lowering unknotting number
Preview AbstractWe explore the relationship between two knot invariants, unknotting number and crosscap number. Specifically, we present two infinite families of knots with a specific crossing change that lowers the unknotting number while raising the crosscap number. One of these families is hyperbolic. This is a non-orientable parallel of Scharlemann and Thompson’s 1988 result for orientable surfaces.