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

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

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