Homotopy of manifolds stabilized by projective spaces
Ruizhi Huang, Stephen Theriault
Abstract
Abstract We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space, and provide concrete examples. To do this, we trace the effect in homotopy theory of surgery on certain product manifolds by showing a loop homotopy decomposition after localization away from the order of the image of the classical ‐homomorphism.
Topics & Concepts
MathematicsHomotopyPure mathematicsRegular homotopyn-connectedComplex projective spaceProjective spaceHomotopy lifting propertyManifold (fluid mechanics)CofibrationQuaternionic projective spaceTopology (electrical circuits)Projective testCombinatoricsMechanical engineeringEngineeringHomotopy and Cohomology in Algebraic TopologyAdvanced Topics in AlgebraAlgebraic structures and combinatorial models