23 citations · 48 across the 8 of their papers we have counts for
8 papers
The mapping class group of connect sums of
Tara Brendle, Nathan Broaddus, Andrew Putman
Let be the connect sum of copies of . A classical theorem of Laudenbach says that the mapping class group is an extension of $\text{Out}…
The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary
Tara Brendle, Nathan Broaddus, Andrew Putman
We give two proofs that appropriately defined congruence subgroups of the mapping class group of a surface with punctures/boundary have enormous amounts of rational cohomology in t…
Finite rigid sets and homologically non-trivial spheres in the curve complex of a surface
Joan Birman, Nathan Broaddus, William Menasco
Aramayona and Leininger have provided a "finite rigid subset" of the curve complex of a surface , characterized by the fact that any si…
Homology of the curve complex and the Steinberg module of the mapping class group
Nathan Broaddus
By the work of Harer, the reduced homology of the complex of curves is a fundamental cohomological object associated to all torsion free finite index subgroups of the mapping class…
Calculating the image of the second Johnson-Morita representation
Joan S. Birman, Tara E. Brendle, Nathan Broaddus
Johnson has defined a surjective homomorphism from the Torelli subgroup of the mapping class group of the surface of genus with one boundary component to , the thir…
The Casson invariant and the word metric on the Torelli group
Nathan Broaddus, Benson Farb, Andrew Putman
We bound the value of the Casson invariant of any integral homology 3-sphere by a constant times the distance-squared to the identity, measured in any word metric on the Torell…
Irreducible Sp-representations and subgroup distortion in the mapping class group
Nathan Broaddus, Benson Farb, Andrew Putman
We prove that various subgroups of the mapping class group of a surface are at least exponentially distorted. Examples include the Torelli group (answering a question…
Noncyclic covers of knot complements
Nathan Broaddus
Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give…