Steven Rosenberg

activity

19972025

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math.DG2024

The Geometry of Loop Spaces IV: Closed Sasakian Manifolds

Yoshiaki Maeda, Steven Rosenberg

We prove that a closed regular $(4 k + 1)$ -Sasakian manifold $(M, h_{0})$ admits a family of non-isometric metrics $h_{ρ}, ρ \geq 0,$ such that $π_{1} (Isom (M, h_{ρ}))$ , the fundamental gr…

math.DG2024

A Codimension Two Approach to the $S^{1}$ -Stability Conjecture

Steven Rosenberg, Jie Xu

J. Rosenberg's $S^{1}$ -stability conjecture states that a closed oriented manifold $X$ admits a positive scalar curvature metric iff $X \times S^{1}$ admits a positive…

math.DG2024

The Geometry of Loop Spaces II: Corrections

Yoshiaki Maeda, Steven Rosenberg, Fabián Torres-Ardila

This paper contains corrections to Madea, Rosenberg, Torres-Ardila, "The Geometry of Loop Spaces II: Characteristic Classes," Advances in Math. (287), 2016, 485-518. The main chang…

The Geometry of Loop Spaces IV: Closed Sasakian Manifolds

A Codimension Two Approach to the S1-Stability Conjecture

The Geometry of Loop Spaces II: Corrections

A Codimension Two Approach to the $S^{1}$ -Stability Conjecture