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Non-slice linear combinations of algebraic knots

Matthew Hedden, Paul Kirk, Charles Livingston (2012)

Journal of the European Mathematical Society

We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.

Observability of control systems for polynomial inputs and genericity

Philippe Jouan (2001)

Applicationes Mathematicae

We consider smooth single-input, two-output systems on a compact manifold X. We show that the set of systems that are observable for any polynomial input whose degree is less than or equal to a given bound contains an open and dense subset of the set of smooth systems.

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