The paper proves a linear volume lower bound for codimension two minimal submanifolds of compact octonionic hyperbolic manifolds, yielding linear waists, systolic freedom, and new lattice fixed point theorems.
Fixed points for actions of Aut(Fn) on CAT(0) spaces
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abstract
For n greater or equal 4 we discuss questions concerning global fixed points for isometric actions of Aut(Fn), the automorphism group of a free group of rank n, on complete CAT(0) spaces. We prove that whenever Aut(Fn) acts by isometries on complete d-dimensional CAT(0) space with d is less than 2 times the integer function of n over 4 and minus 1, then it must fix a point. This property has implications for irreducible representations of Aut(Fn), which are also presented here. For SAut(Fn), the unique subgroup of index two in Aut(Fn), we obtain similar results.
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2024 1verdicts
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Minimal Submanifolds and Waists of Locally Symmetric Spaces
The paper proves a linear volume lower bound for codimension two minimal submanifolds of compact octonionic hyperbolic manifolds, yielding linear waists, systolic freedom, and new lattice fixed point theorems.