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On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature
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abstract
In this paper, we study the fundamental group of the complete steady gradient Ricci soliton with nonnegative sectional curvature. We prove that the fundamental group of such a Ricci soliton is either trivial or infinite. As a corollary, we show that an $n$-dimensional complete $\kappa$-noncollapsed steady gradient Ricci soliton with nonnegative sectional curvature must be diffeomorphic to $\mathbb{R}^n$.
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Infinitely many non-collapsed steady Ricci solitons on complex line bundles
For each k at least 3, the complex line bundle O(k) over CP^{2m+1} admits infinitely many non-collapsed steady Ricci solitons, and for 3 ≤ k ≤ 2m+1 it admits an asymptotically conical Ricci-flat metric.
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