Representations of fundamental groups of 3-manifolds into PGL(3,C): Exact computations in low complexity

In this paper we are interested in computing representations of the fundamental group of a 3-manifold into PSL(3;C) (in particular in PSL(2;C); PSL(3;R) and PU(2; 1)). The representations are obtained by gluing decorated tetrahedra of flags. We list complete computations (giving 0-dimensional or 1-dimensional solution sets) for the first complete hyperbolic non-compact manifolds with finite volume which are obtained gluing less than three tetrahedra with a description of the computer methods used to find them

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold

Assessing Order Effects in Online Community-based Health Forums

Measuring the quality of health content in online health forums is a challenging task. The majority of the existing measures are based on evaluations of forum users and may not be reliable. We employed machine learning techniques, text mining methods, and Big Data platforms to construct four measures of textual quality to automatically determine the similarity of a given answer to professional answers. We then used them to assess the quality of 66,888 answers posted on Yahoo! Answers Health section. All four measures of textual quality revealed a higher quality for asker-selected best answers indicating that askers, to some extent, have a proper judgment to select the best answers. We also studied the presence of order effects in online health forums. Our results suggest that the textual quality of the first answer positively influences the mean textual quality of the subsequent answers and negatively influences the quantity of subsequent answers