Mapping class groups of h-cobordant manifolds

Samuel Muñoz-Echániz

doi:10.1017/fms.2025.10087

January 1, 2025Forum of Mathematics SigmaOpen Access

Mapping class groups of h-cobordant manifolds

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Key Points

The research finds that h-cobordant manifolds can possess different mapping class groups.
Key evidence shows distinct cardinalities among mapping class groups for various h-cobordant manifolds.
Analysis uses a moduli space framework to explore 'h-block' bundles compared to traditional block bundles.
These findings highlight that h-cobordism cannot serve as a reliable invariant for high-dimensional topological structures.

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Implication

Research demonstrates varying mapping class group cardinalities in h-cobordant manifolds, indicating h-cobordism is not an invariant.

Abstract

We prove that the mapping class group is not an h -cobordism invariant of high-dimensional manifolds by exhibiting h -cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli space of ‘ h -block’ bundles and understand its difference with the moduli space of ordinary block bundles.

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Samuel Muñoz-Echániz (2025) studied this question.

synapsesocial.com/papers/68c1c63654b1d3bfb60f1ef1 https://doi.org/10.1017/fms.2025.10087

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Mapping class groups of h-cobordant manifolds

Key Points

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Implication

Abstract

Discussion

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Mapping class groups of h-cobordant manifolds

Key Points

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Implication

Abstract

Discussion

Cite This Study

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