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To what extent are 0-surgeries on fibered knots classifying? Or, exotic $S^2\times S^2$ 's and where we probably shouldn't be looking for them.
Student-Run Research Seminar| Speaker: | Trevor Oliveria-Smith, UC Davis |
| Location: | 3106 Mathematical Science Building |
| Start time: | Wed, Oct 25 2023, 12:10PM |
It is known from the works of Gabai and Teragaitio that 0-surgery on torus knots and the figure-8 knot are characterizing. In general, 0-surgery on a fibered knot K in the 3-sphere does not characterize K. Examples of such knots are constructed using annular twisting techniques yielding non-isotopic knots which 0-surger to the same manifold. Thus, a similar surgery-theoretic characterization to Gabai and Teragaitio for general fibered knots is not possible. In the proposed talk, we conjecture a possible classification using handle-slides and the notion of a dual surgery. By treating surgeries as handle-attachements, the proposed classification has connections to the classification of smooth structures on $S^2\times S^2$.
Our time has changed to 12pm unless speaker wants to stick to 11am time. There will be free pizzas as well:)