Knot Theory and Floer Homology are two interrelated domains in modern mathematical research that bridge topology with sophisticated analytical methods. Knot Theory, historically focused on the ...

Arnold’s work was in an area of mathematics that concerns all the different configurations a physical system like bouncing billiard balls or orbiting planets can take. These configurations are encoded ...

Abstract. We construct the vortex Floer homology group VHF(M, μ; H) for an aspherical Hamiltonian G-manifold (M, ω, μ) and a class of G-invariant Hamiltonian loops Ht, following a proposal of ...

https://doi.org/10.4007/annals.2019.190.3.5 https://www.jstor.org/stable/10.4007/annals.2019.190.3.5 We prove that the map on knot Floer homology induced by a ribbon ...

Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units. The question is deceptively simple: ...

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective. Arnold’s work was in an area of mathematics that ...