On Non-zero Degree Maps between Quasitoric 4-Manifolds

Abstract

We study the map degrees between quasitoric 4-manifolds. Our results rely on Theorems proved by Duan and Wang. We determine the set D (M, N) of all possible map degrees from M to N when M and N are certain quasitoric 4-manifolds. The obtained sets of integers are interesting, e. g. those representable as the sum of two squares D (C P^2#C P^2, C P^2) or the sum of three squares D (C P^2 # C P^2 # C P^2, C P^2). Beside the general results about the map degrees between quasitoric 4-manifolds, the connections among Duan-Wang's approach, the quadratic forms, the number theory and the lattices is established.