Non-invertible knots exist

Invertible calculation's non-invertibility

In cryptosystem theory, it is well-known that a logical mapping that returns the same value that was used as its argument can be inverted with a zero failure probability in linear time. In this paper, however, I show that such a mapping, while trivially assigning a logical state to itself, comes up against an impassable entropy wall such that its computational path is undone inside the threshol...

There Exist Non-trivial Pl Knots Whose Complements Are Homotopy Circles

We show that there exist non-trivial PL knots S n−2 ⊂ S n , n ≥ 5, whose complements have the homotopy type of circles. This is in contrast to the case of smooth, PL locally-flat, and topological locally-flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial. It is well-known that if the complement of a smooth, PL locally-flat, or to...

Transversely Non Simple Knots

By proving a connected sum formula for the Legendrian invariant λ+ in knot Floer homology we exhibit infinitely many transversely non simple knots. Moreover we construct knots admitting many non-isotopic transverse representatives with equal selflinking number.

Invertible polynomial mappings via Newton non-degeneracy

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.

Designated Verification of Non-invertible Watermark