Homotopy of manifolds stabilized by projective spaces

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 J -homomorphism.

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ORCID for Stephen Theriault: orcid.org/0000-0002-7729-5527

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