Degree-one maps onto lens spaces
This paper shows that if \(M\) is a closed orientable 3-manifold then: (1) If there is a degree 1 map to \(L(n,m)\), then \(H_1(M)= Z_n\oplus A\). (2) If \(n>1\) is odd and \(H_1(M)= Z_n\oplus A\), there is a degree one map to an \(L(n,m)\) for some \(m\) with \(\text{gcd} (n,m)=1\). (3) If \(n=2^k(2j+1)\) and \(H_1(M)= Z_n\oplus A\), there is a degree one map to an \(L(n,m)\) for some \(m\) with \(\text{gcd} (n,m)=1\) provided \(A\) contains an even number of \(Z_2k\) summands. Examples are given to show that the assumption on \(A\) is needed for the third result.
scientific article; zbMATH DE number 1025800