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n-Kazhdan groups and higher spectral expanders

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Abstract

Let Γ be a group of type Fn and let X be the n-skeleton of the universal cover of a K(Γ, 1) simplicial complex with finite n-skeleton. We show that if Γ is strongly n-Kazhdan, then for any family of finite index subgroups {Λi}i, the family of simplicial complexes {ΛiX}i are bounded degree n-dimensional spectral expanders. Using this we construct new examples of 2-dimensional spectral expanders.

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Acknowledgements

I thank Anish Ghosh for his encouragement and continued engagement with this project. While I was looking for a higher-dimensional analog of a Cayley graph of a group, Swathi Krishna told me about the Cayley complex. Considering the nth-skeleton of the universal cover of a K(Γ, 1) complex was a small step from there.

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  1. Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India

    Arghya Mondal

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  1. Arghya Mondal
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Mondal, A. n-Kazhdan groups and higher spectral expanders. Isr. J. Math. 258, 453–473 (2023). https://doi.org/10.1007/s11856-023-2480-1

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  • DOI: https://doi.org/10.1007/s11856-023-2480-1

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