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Virtual Legendrian isotopy

Vladimir Chernov;  Rustam Sadykov — 2016

Fundamenta Mathematicae

An elementary stabilization of a Legendrian knot L in the spherical cotangent bundle ST*M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the knot L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. A class of virtual Legendrian isotopy is called a virtual Legendrian knot. In contrast to Legendrian knots, virtual Legendrian knots enjoy the...

On the connectivity of finite subset spaces

Jacob Mostovoy;  Rustam Sadykov — 2012

Fundamenta Mathematicae

We prove that the space e x p k ⋁ S m + 1 of nonempty subsets of cardinality at most k in a bouquet of m+1-dimensional spheres is (m+k-2)-connected. This, as shown by Tuffley, implies that the space e x p k X is (m+k-2)-connected for any m-connected cell complex X.

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