A New Angle on the Stable Homotopy Groups of Spheres Joint Work with Mike Hill and Mike Hopkins University of Rochester Topology Seminar
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چکیده
Determining the stable homotopy groups of spheres has been a vexing and fascinating problem in algebraic topology for the past 70 years. Recall • πn+k(S) is defined to be the set of homotopy classes of maps from S (the unit sphere in R) to S. The set has a natural abelian group structure. • πn+k(S) is known to be independent of n for n > k + 1. We denote this group by π k or πk(S ). • Here are its values for small k. k 0 1 2 3 4 5 6 7 8 9 π k Z Z/2 Z/2 Z/24 0 0 Z/2 Z/240 Z/2 (Z/2) 3
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تاریخ انتشار 2007