February 15, 2024Open Access

Hearing Exotic Smooth Structures: Basic Spectra of Equivariant Manifolds

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Authors

LCLeonardo F. CavenaghiUniversidade Estadual de Campinas (UNICAMP)JÓJoão Marcos Ó LSLlohann D. SperançaShanghai Institute for Science of Science

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Implication

Theoretical analysis reveals invariant, equivariantly isospectral metrics across homeomorphic yet non-diffeomorphic manifolds, indicating scalar curvature cannot distinguish smooth structures.

Key Points

Homeomorphic yet non-diffeomorphic smooth manifolds can support invariant, equivariantly isospectral metrics, establishing such exotic structures on specific homotopy spheres.
Theoretical model analyzing basic eigenvalues of the Riemannian Laplacian under compact Lie group actions identifies matching basic spectra across distinct connected sums.
Highlights that invariant admissible scalar curvature functions fail to differentiate smooth structures, showing identical curvature rings across exotic smooth manifolds.

Cite This Study

Cavenaghi et al. (2024) studied this question.

synapsesocial.com/papers/68e79181b6db643587702ebd https://doi.org/10.48550/arxiv.2402.10106

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Implication

Theoretical analysis reveals invariant, equivariantly isospectral metrics across homeomorphic yet non-diffeomorphic manifolds, indicating scalar curvature cannot distinguish smooth structures.

Hearing Exotic Smooth Structures: Basic Spectra of Equivariant Manifolds

Discussion

Member takes

Implication

Key Points

Cite This Study

Hearing Exotic Smooth Structures: Basic Spectra of Equivariant Manifolds

Discussion

Member takes

Implication

Key Points

Cite This Study

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