542 research outputs found
Higher Teichm\"uller Spaces: from SL(2,R) to other Lie groups
The first part of this paper surveys several characterizations of
Teichm\"uller space as a subset of the space of representation of the
fundamental group of a surface into PSL(2,R). Special emphasis is put on
(bounded) cohomological invariants which generalize when PSL(2,R) is replaced
by a Lie group of Hermitian type. The second part discusses underlying
structures of the two families of higher Teichm\"uller spaces, namely the space
of maximal representations for Lie groups of Hermitian type and the space of
Hitchin representations or positive representations for split real simple Lie
groups.Comment: The file uploaded on May 12th was the wrong one and did not contain
the Section 4.6 that was added. This is the version to appear in the Handbook
of Teichm\"uller theor
Integrality of Volumes of Representations
Let M be an oriented complete hyperbolic n-manifold of finite volume. Using
the definition of volume of a representation previously given by the authors in
[BucherBurgerIozzi2013] we show that the volume of a representation of the
fundamental group of M into the connected component of the isometry group of
hyperbolic n-space, properly normalized, takes integer values if n=2m is at
least 4.
If M is not compact and 3-dimensional, it is known that the volume is not
locally constant. In this case we give explicit examples of representations
with volume as arbitrary as the volume of hyperbolic manifolds obtained from M
via Dehn fillings.Comment: According to the suggestions of the referee, the article has been
almost completely rewritten with the respect to the first versio
Automating Coreference: The Role of Annotated Training Data
We report here on a study of interannotator agreement in the coreference task
as defined by the Message Understanding Conference (MUC-6 and MUC-7). Based on
feedback from annotators, we clarified and simplified the annotation
specification. We then performed an analysis of disagreement among several
annotators, concluding that only 16% of the disagreements represented genuine
disagreement about coreference; the remainder of the cases were mostly
typographical errors or omissions, easily reconciled. Initially, we measured
interannotator agreement in the low 80s for precision and recall. To try to
improve upon this, we ran several experiments. In our final experiment, we
separated the tagging of candidate noun phrases from the linking of actual
coreferring expressions. This method shows promise - interannotator agreement
climbed to the low 90s - but it needs more extensive validation. These results
position the research community to broaden the coreference task to multiple
languages, and possibly to different kinds of coreference.Comment: 4 pages, 5 figures. To appear in the AAAI Spring Symposium on
Applying Machine Learning to Discourse Processing. The Alembic Workbench
annotation tool described in this paper is available at
http://www.mitre.org/resources/centers/advanced_info/g04h/workbench.htm
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