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We study random 2-dimensional complexes in the Linial-Meshulam model and prove that for the probability parameter satisfying p ≪ n −46/47 a random 2-complex Y contains several pairwise disjoint tetrahedra such that the 2-complex Z obtained by removing any face from each of these tetrahedra is aspherical. Moreover, we prove that the obtained complex Z… (More)

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