Abstract
We give a lattice construction of the discretizations of the topologically nontrivial maps S2n−1→S n . For n=1, 2, 4, 8, these are the Hopf maps. The construction, based on Barnes-Wall lattices, Reed-Muller error-correcting codes, and Hadamard matrices, generalizes to n=2 i for i any integer. Manton's result for the cases n=2 and 4 (i.e., the monopole and instanton) are included. We argue that discrete harmonic analysis will be exact in the infinite dimension limit.
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