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Math Review to the pap er M. Atapour, C. E. Soteros, D. W. Sumners and S. G. Whittington, `Counting closed 2-manifolds in tubes in hypercubic lattices', Journal of Physics A: Mathematical and Theoretical, 48 (2015). This is a paper on pure mathematics (geometry and topology) motivated by physics. The authors study asymptotic behavior of closed connected 2-manifolds in the union of 2-dimensional faces of the standard cubic lattice in d-dimensional Euclidean space Rd . E.g. for each d 3 and L there are , > 0 such that the number of polyhedral spheres · formed by n two-dimensional faces of the standard cubic lattice in Rd , · whose vertices satisfy inequalities x1 0, 0 x2 L, . . . , 0 xd L, · who have a vertex for which x1 = 0, is asymptotically equivalent to n (Theorem 4). Same result (with different , ) holds for `polyhedral spheres' replaced by `closed connected 2-dimensional manifolds' (Theorem 5). The authors also show that · manifolds with any fixed genus, · orientable manifolds for d 4, and · unknotted manifolds are exponentially rare (Theorems 6-9). The statements and proofs are not up to mathematical standards, so there appears an interesting task of writing rigorous statements and proofs.