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.
Bounded quotients of the fundamental group of a random 2-complex
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abstract
Let D denote the (n-1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of D obtained by starting with the full 1-skeleton of D and then adding each 2-simplex independently with probability p. For a fixed c>0 it is shown that if p=\frac{(6+7c) \log n}{n} then a.a.s. the fundamental group \pi(Y) does not have a nontrivial quotient of order at most n^c.
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math.DG 1years
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.