Mapping class groups of h-cobordant manifolds
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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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Acknowledgements: The author is immensely grateful to his PhD supervisor, Oscar Randal-Williams, for suggesting this problem and for many illuminating discussions that have greatly benefited this work. He would also like to thank Connor Malin for originally raising the question in [Mal21], the anonymous referee for valuable feedback and corrections, John Nicholson for making him aware of [ZTC19], and Sander Kupers, Robin Stoll and Henry Wilton for further helpful comments.
Publication status: Published
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2050-5094
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