Fibrations on the 6sphere
Fibrations on the 6sphere

Jeff Viaclovsky, UC Irvine
Fine Hall 314
Let Z be a compact, connected 3dimensional complex manifold with vanishing first and second Betti numbers and nonvanishing Euler characteristic. We prove that there is no holomorphic mapping from Z onto any 2dimensional complex space. Combining this with a result of CampanaDemaillyPeternell, a corollary is that any holomorphic mapping from the 6dimensional sphere S^6, endowed with any hypothetical complex structure, to a strictly lowerdimensional complex space must be constant. In other words, there does not exist any holomorphic fibration on S^6. This is joint work with Nobuhiro Honda.