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On the connectivity of finite subset spaces

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Mostovoy J., Sadykov R.

Fundamenta Mathematicae

2012

tom 217

nr 3

279-282

We prove that the space $exp_k ⋁ S^{m+1}$ 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 $exp_k X$ is (m+k-2)-connected for any m-connected cell complex X.

Virtual Legendrian isotopy

100%

Chernov V., Sadykov R.

Fundamenta Mathematicae

2016

tom 234

nr 2

127-137

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 property that there is a bijective correspondence between the virtual Legendrian knots and the equivalence classes of Gauss diagrams. We study virtual Legendrian knots and show that every such class contains a unique irreducible representative. In particular we get a solution to the following conjecture of Cahn, Levi and the first author: two Legendrian knots in ST*S² that are isotopic as virtual Legendrian knots must be Legendrian isotopic in ST*S².

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Sadykov R.

1 Chernov V.

1 Mostovoy J.

1 2016

1 2012

Wyniki wyszukiwania

On the connectivity of finite subset spaces

Virtual Legendrian isotopy