%0 Journal Article %T Milnor-Wood inequalities for products %A Michelle Bucher %A Tsachik Gelander %J Mathematics %D 2012 %I arXiv %R 10.2140/agt.2013.13.1733 %X We prove Milnor-Wood inequalities for local products of manifolds. As a consequence, we establish the generalized Chern Conjecture for products $M\times \Sigma^k$ for any product of a manifold $M$ with a product of $k$ copies of a surface $\Sigma$ for $k$ sufficiently large. %U http://arxiv.org/abs/1201.0332v1