Lefschetz pencils and mapping class groups
نویسنده
چکیده
Holomorphic maps between complex manifolds have many properties which distinguish them among general smooth maps. Consider, for example, the case of a map between Riemann surfaces. A holomorphic map is represented locally, in suitable co-ordinates, by one of the models z 7→ z for k ≥ 0. These models are very different from the models of generic smooth maps between surfaces, which are, in addition to the points where the map is a local diffeomorphism, folds and cusps. It is interesting to see what happens if we perturb the holomorphic map z 7→ z by a small non-holomorphic term. So for > 0 we define f ( ) : C → C by
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