Setup. Say we have a germ of a holomorphic function $f:(\mathbb C^{n+1},0)\to (\mathbb C,0)$ with a critical point at the origin. There is an $\epsilon>0$ small enough so that $f$ becomes a fibration when restricted to $$g=f/|f|:S_\epsilon^{2n+1}\setminus f^{-1}(0)\to S^1.$$ The fibres of $g$ are diffeomorphic to one another, and each of them is called a Milnor fibre of $f$ at $0\in\mathbb C^{n+1}$.
In the Introduction of these notes on vanishing cycles, the author states:
"The cohomology of the Milnor fibre is known to be nonzero in degrees between $0$ and $n$ at most [$\dots$]"
In the next paragraph, the author states that the Milnor fiber $F$ of an isolated singular point has the same homotopy type of a bouquet of $\mu(f)$ spheres, where $\mu(f)$ is the Milnor number of $f$, namely the dimension of the vector space $\mathbb C[[x_0,\dots,x_n]]/(\textrm{Jac}(f))$. In particular, this implies that $H^n(F,\mathbb C)=\mathbb C^{\mu(f)}$, but also that $$H^i(F,\mathbb C)=0,\,\,\,\textrm{if }0<i<n.$$
Question 1. Does not this seem to contradict the previous quoted assertion?
Question 2. Am I right in thinking that the cohomology of the Milnor fiber at a regular point of $f^{-1}(0)$ is in fact zero in all degrees?
Thank you in advance.