Index and nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces Filippo Morabito 58E1249Q0553A10indexnullityJacobi operatorCosta-Hoffman-Meeks surfaces The aim of this work is to extend the results of S. Nayatani about the index and the nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces for values of the genus bigger than $37$. That allows us to state that these minimal surfaces are non degenerate for all the values of the genus in the sense of the definition of J. P\'erez and A. Ros. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3476 10.1512/iumj.2009.58.3476 en Indiana Univ. Math. J. 58 (2009) 677 - 708 state-of-the-art mathematics http://iumj.org/access/