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Real flexible knots and real symplectic knots.
by
Johan Björklund
University of Gävle
In this talk we will define flexible knots, objects meant to capture the topological properties of real algebraic knots, and then use them to introduce flexible isotopy, that is, an isotopy which is at all times a flexible knot.
Flexible knots (and links) are less rigid than real algebraic knots. This lack of rigidity allows a complete classification (up to flexible isotopy) utilizing some basic invariants together with Viro's encomplexed writhe.
Since we have a complete classification on the flexible level, any new rigid isotopy invariant for real algebraic knots must then utilize more of the algebraic geometric structure and not use the smooth topology.
If time allows we will discuss real symplectic knots, which have more structure, and so are closer to the real algebraic knots. This is work in progress with Georgios Dimitroglou-Rizell.
Date received: April 23, 2018
Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cboy-28.