Exotic $\mathbb{R}^4$'s and positive isotropic curvature

Hong Huang

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arXiv · 1605.00965

Exotic $\mathbb{R}^4$'s and positive isotropic curvature

Hong Huang

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Abstract

We show that no exotic $\mathbb{R}^4$ admits a complete Riemannian metric with uniformly positive isotropic curvature and with bounded geometry. This is essentially a corollary of the main result in [Hu1], and was stated in [Hu2] without proof. In the process of the proof we also show that the diffeomorphism type of an infinite connected sum of some connected smooth $n$-manifolds ($n\geq 2$) according to a locally finite graph does not depend on the gluing maps used.

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Hong Huang. 2016-05-03. Exotic $\mathbb{R}^4$'s and positive isotropic curvature. https://arxiv.org/abs/1605.00965

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