From cef1e9e12e49974e7bb63be286baffa7d09d7af8 Mon Sep 17 00:00:00 2001 From: filippomazzoli Date: Wed, 7 Aug 2024 20:49:16 -0700 Subject: [PATCH] Update papers.bib --- _bibliography/papers.bib | 3 +++ 1 file changed, 3 insertions(+) diff --git a/_bibliography/papers.bib b/_bibliography/papers.bib index 37baf1c..39baf5a 100644 --- a/_bibliography/papers.bib +++ b/_bibliography/papers.bib @@ -17,6 +17,7 @@ @ARTICLE{2023diam_vol_entr adsnote = {Provided by the SAO/NASA Astrophysics Data System}, abstract = {We investigate properties of the pseudo-Riemannian volume, entropy, and diameter for convex cocompact representations \(\rho : \Gamma \to {\mathrm S \mathrm O}(p,q+1)\) of closed \(p\)-manifold groups. In particular: We provide a uniform lower bound of the product entropy times volume that depends only on the geometry of the abstract group \(\Gamma\). We prove that the entropy is bounded from above by \(p-1\) with equality if and only if \(\rho\) is conjugate to a representation inside \({\mathrm S}({\mathrm O}(p,1)\times{\mathrm O}(q))\), which answers affirmatively to a question of Glorieux and Monclair. Lastly, we prove finiteness and compactness results for groups admitting convex cocompact representations with bounded diameter.}, html= {https://arxiv.org/abs/2312.17137}, + year-preprint={2023}, } @ARTICLE{2019constantgaussian, @@ -190,6 +191,7 @@ @ARTICLE{2023pleated abstract = {In this article, we single out representations of surface groups into \({\mathsf P \mathsf S \mathsf L}_d({\mathbb C})\,\,\) which generalize the well-studied family of pleated surfaces into \({\mathsf P \mathsf S \mathsf L}_2({\mathbb C})\). Our representations arise as sufficiently generic \(\lambda\)-Borel Anosov representations, which are representations that are Borel Anosov with respect to a maximal geodesic lamination \(\lambda\). For fixed \(\lambda\,\,\) and \(d \), we provide a holomorphic parametrization of the space \({\mathcal R}(\lambda,d)\,\, \) of \((\lambda,d)\)-pleated surfaces which extends both work of Bonahon for pleated surfaces and Bonahon and Dreyer for Hitchin representations.}, html={https://arxiv.org/abs/2305.11780}, keywords={preprint}, + year-preprint={2023}, } @@ -233,4 +235,5 @@ @ARTICLE{2016intertwining abstract= {In arXiv:0707.2151 the authors introduced the theory of local representations of the quantum Teichmüller space \(\mathcal T^q_S \,\) (\(q\,\,\) being a fixed primitive \(N\)-th root of \( (-1)^{N + 1} \)) and they studied the behaviour of the intertwining operators in this theory. One of the main results [Theorem 20, arXiv:0707.2151] was the possibility to select one distinguished operator (up to scalar multiplication) for every choice of a surface \(S\), ideal triangulations \(\lambda, \lambda'\,\,\) and isomorphic local representations \(\rho, \rho'\), requiring that the whole family of operators verifies certain Fusion and Composition properties. By analyzing the constructions of arXiv:0707.2151, we found a difficulty that we eventually fix by a slightly weaker (but actually optimal) selection procedure. In fact, for every choice of a surface \(S\), ideal triangulations \(\lambda, \lambda'\,\,\) and isomorphic local representations \(\rho, \rho'\), we select a finite set of intertwining operators, naturally endowed with a structure of affine space over \(H_1(S;{\mathbb Z}_N) \,\) (\({\mathbb Z}_N \,\,\) is the cyclic group of order \(N\)), in such a way that the whole family of operators verifies augmented Fusion and Composition properties, which incorporate the explicit behavior of the \({\mathbb Z}_N\)-actions with respect to such properties. Moreover, this family is minimal among the collections of operators verifying the weak Fusion and Composition rules (in practice the ones considered in arXiv:0707.2151). In addition, we adapt the derivation of the invariants for pseudo-Anosov diffeomorphisms and their hyperbolic mapping tori made in arXiv:0707.2151 and arXiv:math/0407086 by using our distinguished family of intertwining operators.}, html={https://arxiv.org/abs/1610.06056}, keywords={preprint}, + year-preprint={2016}, }