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Tara E. Brendle
My research is on braid groups, mapping class groups, and
related structures. Here I have grouped my papers and
book chapters roughly according to topics of particular
focus, though there is a bit of overlap. A list of my
publications in reverse chronological order can be found on
my listing in Enlighten,
the University of Glasgow's online repository.
Mapping class groups in a dimension other than 2:
- The mapping
class group of connect sums of S2 x S1. (pdf)
w/ Nathan Broaddus and Andrew Putman
Combinatorial
models for
mapping class groups (curve
complexes):
- The high-dimensional cohomology of the moduli space of
curves with level structures II: punctures and boundary. (pdf)
w/ Nathan Broaddus and Andrew Putman
- Normal
subgroups of mapping class groups and the
metaconjecture of Ivanov. (pdf)
w/ Dan Margalit
J. of the Amer. Math. Soc., 32 (2019), 1009-1070.
- Commensurations
of the Johnson kernel. (pdf)
w/ Dan Margalit
Geometry and Topology, 8 (2004), 1361-1384.
- Addendum to: Commensurations of the Johnson
kernel. (pdf)
w/ Dan Margalit
Geometry and Topology, 12 (2008), 97-101.
- Erratum
to: Commensurations of the
Johnson kernel. (pdf)
w/ Dan Margalit
To appear in Geometry & Topology.
Braid groups:
- Congruence subgroups of braid
groups. (pdf)
Winter Braids VIII, Lecture Notes Vol. 5 (2018), 1-26.
- The level four braid
group. (pdf)
w/ Dan Margalit
Journal für die reine und angewandte Mathematik
(Crelle's Journal), 735 (2018), 249-264.
- Erratum
to: The level four braid group. (pdf)
w/ Dan Margalit
- Generators
for the hyperelliptic Torelli group and the kernel
of the Burau representation at t = -1.
(pdf)
w/ Dan Margalit and Andrew Putman
Inventiones Mathematicae, 200, No. 1 (2015),
263-310.
- Configuration
spaces of rings and wickets. (pdf)
w/ Allen Hatcher
Commentarii Math. Helv. 88 (2013),
131-162.
- Braids:
A Survey. (pdf)
w/ Joan Birman
Handbook of Knot Theory, ed. W. Menasco and
M. Thistlethwaite (2005).
Torelli
groups:
- Calculating
the image of the second Johnson-Morita
representation. (pdf)
w/ Joan S. Birman and Nathan Broaddus
Advanced Studies in Pure Mathematics (2008),
“Groups of Diffeomorphisms” (in honor of Shigeyuki
Morita).
- The
Birman-Craggs-Johnson homomorphism and abelian
cycles in the Torelli group. (pdf)
w/ Benson Farb
Mathematische Annalen 338, No. 1 (2007), ,
33-53.
- The
Torelli group and representations of the mapping
class group. (pdf)
Doctoral Thesis, Columbia University,
(2002).
Hyperelliptic Torelli groups:
- The level four braid
group. (pdf)
w/ Dan Margalit
Journal für die reine und angewandte Mathematik
(Crelle's Journal), 735 (2018), 249-264.
- Generators
for the hyperelliptic Torelli group and the kernel
of the Burau representation at t = -1.
(pdf)
w/ Dan Margalit and Andrew Putman
Inventiones Mathematicae, 200, No. 1 (2015),
263-310.
- Factoring
in the hyperelliptic Torelli group. (pdf,
pdf (version 1))
w/ Dan Margalit
Mathematical Proceedings of the Cambridge
Philosophical Society, 159, Issue 02 (2015),
207-217.
- Point
pushing, homology, and the hyperelliptic
involution. (pdf)
w/ Dan Margalit
Michigan Mathematical Journal, 62 (2013),
451-473.
- Cohomology
of the hyperelliptic Torelli group. (pdf)
w/ Leah Childers and Dan Margalit
Israel Journal of Mathematics, 195 (2013),
613-630.
Mapping
class groups:
- Every
mapping class group is generated by 6 involutions.
(pdf)
w/ Benson Farb
Journal of Algebra, 278 (2004), 187-198.
- The
Torelli group and representations of the mapping
class group. (pdf)
Doctoral Thesis, Columbia University,
(2002).
- On
the linearity problem for mapping class groups.
(pdf)
w/ Hessam Hamidi-Tehrani,
Algebraic and Geometric Topology, 1 (2001),
445-468.
Book
Chapters:
- Mapping class groups.
(an
old version-pdf)
(w/ Leah Childers and Dan Margalit).
Office Hours with a Geometric Group
Theorist, ed. M. Clay and D. Margalit (Princeton
University Press), (2017).
- Braids:
A Survey. (pdf)
w/ Joan Birman
Handbook of Knot Theory, ed. W. Menasco and M.
Thistlethwaite (2005).
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