Why does superglue ignite cotton?
Though the monomers in cyanoacrylate glues contain an ester, their polymerization doesn't rely on that ester group directly.  The Wikipedia article for cyanoacrylates shows the polymerization more clearly than I can easily explain in words.  The many hydroxyl groups in cellulose do start polymerization effectively, and the large surface area of cotton wool provides a large number of sites for the glue to cure.

When I read your question I was curious; I had never heard of this before.  I searched the internet and was only able to find one or two examples of people actually trying this successfully, and both of them looked dubious.  I've spilled superglue on cotton shirts and pants any number of times and while it cures almost instantly, it has never caught my shirt on fire.  

I decided to try it myself, and I soaked a cotton ball in superglue to see what would happen.  The glue cured extremely rapidly, producing very irritating (colorless) fumes, and the mass of glue and cotton got warm, but it was nowhere near hot enough to ignite - my tap runs hotter than the glue got.  There may be a particular type of glue that cures significantly more exothermically, but I'm inclined to think that this is an internet hoax, and Popular Science agrees.