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- W2775442078 abstract "Let $M$ be a closed spin manifold which supports a positive scalar curvature metric. The set of concordance classes of positive scalar curvature metrics on $M$ forms an abelian group $P(M)$ after fixing a positive scalar curvature metric. The group $P(M)$ measures the size of the space of positive scalar curvature metrics on $M$. Weinberger and Yu gave a lower bound of the rank of $P(M)$ in terms of the number of torsion elements of $pi_1(M)$. In this paper, we give a sharper lower bound of the rank of $P(M)$ by studying the image of the relative higher index map from $P(M)$ to the real K-theory of the group $mathrm{C}^ast$-algebra $mathrm{C}^ast_{mathrm{r}}(pi_1(M))$. We show that it rationally contains the image of the Baum-Connes assembly map up to a certain homological degree depending on the dimension of $M$. At the same time we obtain lower bounds for the positive scalar curvature bordism group by applying the higher rho-invariant." @default.
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- W2775442078 date "2021-10-01" @default.
- W2775442078 modified "2023-10-18" @default.
- W2775442078 title "On the range of the relative higher index and the higher rho-invariant for positive scalar curvature" @default.
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- W2775442078 doi "https://doi.org/10.1016/j.aim.2021.107897" @default.
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