TITLE: Classification of lens space
QUESTION [7 upvotes]: Let $L(p,q)$ be the lens space, that is $L(p,q)=S^3/\mathbb{Z}_p$. 
Here, $\mathbb{Z}_p$ acts on $S^3$ by $(z_1,z_2)\mapsto (\rho z_1,\rho^q z_2)$, $ \rho=e^{\frac{2\pi i}{p}}$.
It is well known that 
$L(p,q)$ and $L(p',q')$ are diffeomorphic if and only if $p'=p, q'=\pm q^{\pm1}$ (mod $p$).
In A. Hatcher's note page 39-42, there is a proof of the above classification theorem of lens space using the uniqueness of Heegaard torus in Lens space up to isotopy. But I have some misunderstandings with his argument when I following it line by line. 
Where can I find the original proof of classification of Lens space by using uniqueness of Heegaard torus up to isotopy? 
Note : I know that there is a proof that uses whitehead torsion of lens space and its invariance under the homeomorphism which I already familiar sufficiently.

REPLY [7 votes]: The proof that Hatcher presents is due to Bonahon and Otal.  The reference is here:
MR0663085 (83f:57008)
Bonahon, Francis; Otal, Jean-Pierre
Scindements de Heegaard des espaces lenticulaires. (French. English summary) [Heegaard splittings of lens spaces]
C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 17, 585–587.
57N10
If I recall, I believe Hatcher's write-up is similarly detailed to Bonahon and Otal's argument.  And there are steps missing in both presentations but they're readily filled.