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7. Explicit contact handlebodies


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      Problem 7.1.

      [Breen] Give a bypass description of convex surfaces foliating the region in $(S^5,\xi_k):=\text{OBD}(T^*S^2, \tau^{2k+1})$ between two Darboux balls.


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          Problem 7.2.

          Find other interesting explicit bypass decompositions of contact manifolds.


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              Problem 7.3.

              [Murphy] Can we characterize trivial bypasses in terms of the belt sphere of $n$-handle and the attaching sphere of the $n+1$ handle?


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                  Problem 7.4.

                  Can triviality be detected via capacities on balls around the intersection point?


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                      Problem 7.5.

                      [Murphy] Understand contact connected sum in high dimensions: can non-standard structures on $S^5$ connect sum to give $\xi_{std}$?


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                          Problem 7.6.

                          Does connected sum preserve tightness?


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                              Problem 7.7.

                              Can non-destabilizable OBDs connect sum to a destabilizable (or otherwise non-minimal) OBD?

                                  Cite this as: AimPL: Higher-dimensional contact topology, available at http://aimpl.org/highdimcontacttop.