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Learning from the masters: four lessons from Oleg
by
Jozef H. Przytycki
George Washington University,
(1) Pachner moves: At the beginning of his stay in Riverside, in Spring of 1992, Oleg brought a news about Pachner moves (just add an (n+1)-simplex to the boundary of triangulated (n+1)-manifold (M=∂W). A modification of a triangulation of M is a Pachner move).
(2) Khovanov homology: Oleg gave "Jankowski talk" in Gdansk in 2002, and at seminar after explained us his understanding of Khovanov homology. It was enlightenment for us. Being a skein module person I started thinking on categorification of links in F ×[0, 1].
(3) Finite topological spaces: Oleg gave Colloquium at GWU (2007) and started with a puzzle - compute fundamental group of the following 4-element topological space (X, T). X={a, b, c, d}, T={∅, {b}, {c}, {b, c}, {a, b, c}, {b, c, d}, X}. We looked with surprise: 4-element topological space with interesting fundamental group? At the end of the lecture Oleg commented `if you got Z, it is good'. From that time I devote part of my General Topology class on finite topological spaces. I even noticed that their topology always comes from some hemimetric.
(4) Vladimir A Rochlin: This is most important, of moral character, and concerns Oleg's advisor. Rochlin was dismissed from his job suddenly... But Oleg should tell us this story.
Date received: May 1, 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-41.