There is a result for the dimension bound for $\bar{M_{g,n}}/S_n$, (this is moduli space for Riemann surface of genus $g$ with $n$ marked points) that is $H_{i}(\bar{M_{g,n}}/S_n)=0$, for $i\ge 6g-7+2n$. This result (see Costello: Gromov-Witten potential associated to a TCFT) can be derived from virtual cohomology dimension of mapping class group (see J. L. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math). I am wondering if there is such kind of theorem for surface with boundary, for example, is there any similar results for mapping class group of orientable surface with boundary(and marked points if necessary). Then can we get a similar result of the above dimension bound for moduli space of Riemann surface with boundary and marked points? I just want to see if such a kind of result already exist.