An equivalent description of the lens space L(p,q) with p prime.

In the paper, we give an equivalent description of the lens space L (p , q) with p prime in terms of any corresponding Heegaard diagrams as follows: Let M be a closed orientable 3-manifold with π 1 (M) ≠ 1 , and U ∪ F V a Heegaard splitting of genus n for M with an associated Heegaard diagram (U ; J 1 , ... , J n). Assume p is a prime integer. Then M is homeomorphic to the lens space L (p , q) if and only if there exists an embedding f : U ↪ L (p , q) such that L = { f (J 1) , ... , f (J n) } bounds a complete system of surfaces for W = L (p , q) \ f (U) ¯. [ABSTRACT FROM AUTHOR]