摘要
We discuss a possible definition for“k-width”of a closed d-manifold Md,and on embedding Md e↪ℝn,n>d≥k,generalizing the classical notion of width of a knot.We show that for every 3-manifold 2-width(M3)≤2 but that there are embeddings ei∶T3↪ℝ4 with 2-width(ei)→∞.We explain how the divergence of 2-width of embeddings offers a tool to which might prove the Goeritz groups Gg infinitely generated for g≥4.Finally we construct a homomorphismg∶Gg→MCG(#g S2×S2),suggesting a potential application of 2-width to 4D mapping class groups.
基金
funded by the"Microsoft Research","Aspen Center for Physics"and"UCSB".
