Steven Rosenberg

collaborators

3 papers

math.DG2026

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.DG2025

The Geometry of Loop Spaces V: Fundamental Groups of Geometric Transformation Groups

Yoshiaki Maeda, Steven Rosenberg

We use differential forms on loop spaces to prove that the fundamental group of certain geometric transformation groups is infinite. Examples include both finite and infinite dimen…

math.DG2025

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 $h_{I ¨} , I ¨ \geq 0,$ such that $I ¨ _{1} (Isom (M, h_{I ¨} ))$ , the fundamenta…

A Codimension Two Approach to the S1-Stability Conjecture

The Geometry of Loop Spaces V: Fundamental Groups of Geometric Transformation Groups

The Geometry of Loop Spaces IV: Closed Sasakian Manifolds

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