Education and Employment
- 2015-present, Associate Professor, Ohio State University
- 2009-2015, Assistant Professor, Ohio State University
- 2005-2009, L.E. Dickson Postdoctoral Instructor, University of Chicago
- 2003-2005, H.C. Wang Assistant Professor, Cornell University
- 1997-2003, Ph.D. Mathematics, Columbia University
- 1993-1997, B.S. Mathematics, University of Chicago
Publications
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T. E. Brendle, N. Broaddus and A. Putman, The mapping class group of connect sums of S2xS1. Submitted.
| arXiv |
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T. E. Brendle, N. Broaddus and A. Putman, The high-dimensional cohomology of the moduli space of curves with level
structures II: punctures and boundary. Submitted. | arXiv |
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J. Birman, N. Broaddus and W. Menasco, Finite
rigid sets and homologically nontrivial spheres in the curve complex of a surface,
J. Topol. Anal. 7 (2015), no. 1, 47—71. | MathSciNet
Review | arXiv |
The authors answer a question of Aramayona and Leininger on the homological
nontriviality of certain “finite rigid” simplicial subcomplexes of the curve
complex.
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N. Broaddus,
Homology of the curve
complex and the Steinberg module of the mapping class group, Duke Math. J.
161 (2012), no. 10, 1943—1969. | MathSciNet
Review | arXiv |
Building on the work of Harer, I investigate the virtual dualizing module
of the mapping class group which is also the homology group of the complex
of curves. The main result is that as a module over the group ring
of the mapping class group, the homology of the curve complex is generated by
a single element.
- N. Broaddus, B. Farb and A. Putman,
Irreducible Sp-representations
and subgroup distortion in the mapping class group, Comment. Math. Helv.
86 (2011), no. 3, 537—556. | MathSciNet
Review | arXiv |
We develop a general tool for demonstrating exponential
distortion of the word metric of a finitely generated subgroup of a finitely
generated supergroup. We then use this tool to show that a number of
subgroups of the mapping class group of a surface are at least exponentially
distorted. In particular the Torelli subgroup of the mapping class group is
at least exponentially distorted.
- J. S. Birman, T. E. Brendle and N. Broaddus, Calculating the image of the
second Johnson-Morita representation, in Groups of Diffeomorphisms:
in honor of Shigeyuki Morita on the occasion of his 60th birthday,
119—134. (2008) | MathSciNet
Review | arXiv |
The exact homomorphic image of the mapping class group under an extension
of the Johnson homomorphism—which had
been previously identified by S. Morita up to finite index—is given. This result is
part of a program to use representations of the mapping class group to
compute invariants of Heegaard splittings of 3-manifolds.
- N. Broaddus, B. Farb and A. Putman, The
Casson invariant and the word metric on the Torelli group, C. R. Math.
Acad. Sci. Paris (2007), no. 8, 449—452. | MathSciNet
Review | arXiv |
The square of the word length in the Torelli group gives a tight upper
bound on the size of the Casson invariant of a homology 3-sphere.
- N. Broaddus, Noncyclic
covers of knot complements, Geom. Dedicata 111 (2005), 211—239.
| MathSciNet
Review | arXiv |
An upper bound is given on the number of sheets in the smallest finite noncyclic cover of
the complement of a nontrivial knot.
