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This work focuses on important step in quantitative topology: given homotopic mappings from S^m to S^n of Lipschitz constant L, build the (asymptotically) simplest homotopy between them (meaning having the least Lipschitz constant). The present paper resolves this problem for the first case where Hopf invariant plays a role: m = 3, n = 2, constructing a homotopy with Lipschitz constant O(L).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
