Connected sums with HP^n or CaP^2 and the Yamabe invariant - Mathematics > Differential GeometryReport as inadecuate




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Abstract: Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $YM$ isnonpositive. We show that $$YM\sharp l \Bbb HP^k\sharp m \bar{\BbbHP^k}=YM,$$ where $l,m$ are nonnegative integers, and $\Bbb HP^k$ is thequaternionic projective space. When $k=4$, we also have $$YM\sharp lCaP^2\sharp m \bar{CaP^2}=YM,$$ where $CaP^2$ is the Cayley plane.



Author: Chanyoung Sung

Source: https://arxiv.org/



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