Detecting exotic spheres in low dimensions using coker <i>J</i>
Mark Behrens, Michael A. Hill, Michael J. Hopkins, Mark Mahowald
Abstract
Building off of the work of Kervaire–Milnor and Hill–Hopkins–Ravenel, Wang and Xu showed that the only odd dimensions n for which S n has a unique differentiable structure are 1, 3, 5, and 61. We show that the only even dimensions below 140 for which S n has a unique differentiable structure are 2, 6, 12, 56, and perhaps 4.
Topics & Concepts
Coker unitDifferentiable functionSPHERESPure mathematicsWork (physics)MathematicsSeparate spheresPhysicsChemistryPolitical scienceLawThermodynamicsOrganic chemistryAstronomyIdeologyCokePoliticsHomotopy and Cohomology in Algebraic TopologyBlack Holes and Theoretical PhysicsGeometric and Algebraic Topology