$n$-Kazhdan groups and higher spectral expanders

Arghya Mondal

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n-Kazhdan groups and higher spectral expanders

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arxiv 2112.09431 v2 pith:QVG2MBOY submitted 2021-12-17 math.GR

n-Kazhdan groups and higher spectral expanders

Arghya Mondal This is my paper

classification math.GR

keywords expandersgammaspectraldimensionalfamilyfinitekazhdanlambda

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

n-Kazhdan groups and higher spectral expanders

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