Positive curvature and discrete abelian symmetry

Lee Kennard; Elahe Khalili Samani; Catherine Searle

doi:10.1007/s00208-026-03509-2

July 16, 2026Mathematische AnnalenOpen Access

Positive curvature and discrete abelian symmetry

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Key Points

To generalize symmetry results for positively curved manifolds by replacing the torus with an elementary abelian two-group.
Utilized mathematical frameworks concerning manifolds with positive curvature.
Applied concepts of abelian groups to expand previous symmetry findings.
Generalized Grove and Searle’s maximal symmetry result for positively curved manifolds.
Updated Wilking’s half-maximal symmetry result within the context of abelian groups.

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Implication

This research generalizes symmetry results for positively curved manifolds with an isometric action by using an elementary abelian two-group.

Abstract

By replacing the torus with an elementary abelian two-group, we generalize Grove and Searle’s maximal symmetry result and Wilking’s half-maximal symmetry result for positively curved manifolds with an isometric torus action.

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Kennard et al. (2026) studied this question.

synapsesocial.com/papers/6a5b16f018557b26c20394b1 https://doi.org/10.1007/s00208-026-03509-2

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Positive curvature and discrete abelian symmetry

Key Points

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Implication

Abstract

Discussion

Cite This Study

Positive curvature and discrete abelian symmetry

Key Points

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Implication

Abstract

Discussion

Cite This Study

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