On the Simplicial Volumes of Fiber Bundles
نویسنده
چکیده
We show that surface bundles over surfaces with base and fiber of genus at least 2 have non-vanishing simplicial volume. The simplicial volume ||M ||, introduced by Gromov [3], is a homotopy invariant which measures the complexity of the fundamental class of an oriented manifold M . It is determined by the classifying map of the universal covering, and tends to be non-zero for large manifolds or fundamental groups, typically the negatively curved ones. For products of compact oriented manifolds Gromov [3] proved that the simplicial volume is essentially multiplicative. More precisely, there are universal positive constants cn depending only on n = dim(M1 × M2) such that ||M1 ×M2|| ≤ cn||M1|| · ||M2|| , (1)
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