Geodesic
The fourth tautological group of $\overline{\mathfrak{M}}_{g,n}$ and relations with the cohomology
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 2, pp. 137-168 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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We give a complete description of the fourth tautological group of the moduli space of pointed stable curves, $\overline{\mathfrak{M}}_{g,n}$, and prove that for $g \ge 8$ it coincides with the cohomology group with rational coefficients. We further give a conjectural upper bound depending on the genus for the degree of new tautological relations. 
@article{RLIN_2003_9_14_2_a3,
     author = {Polito, Marzia},
     title = {The fourth tautological group of $\overline{\mathfrak{M}}_{g,n}$ and relations with the cohomology},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {137--168},
     year = {2003},
     volume = {Ser. 9, 14},
     number = {2},
     zbl = {1177.14056},
     mrnumber = {MR2053662},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_2_a3/}
}
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Polito, Marzia. The fourth tautological group of $\overline{\mathfrak{M}}_{g,n}$ and relations with the cohomology. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 2, pp. 137-168. http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_2_a3/