Homotopy of manifolds stabilized by projective spaces

Ruizhi Huang; Stephen Theriault

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arXiv · 2204.04368

Homotopy of manifolds stabilized by projective spaces

Ruizhi Huang·Stephen Theriault

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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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Ruizhi Huang, Stephen Theriault. 2022-04-09. Homotopy of manifolds stabilized by projective spaces. https://arxiv.org/abs/2204.04368

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