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2,016 results on '"Lee, In-Seon"'

1. Cusped Borel Anosov representations with positivity

Author

Zhang, Tengren and Lee, Gye-Seon

Subjects
Mathematics - Differential Geometry, Mathematics - Group Theory, 22E40, 20H10, 57M60
Abstract

We show that if a cusped Borel Anosov representation from a lattice $\Gamma \subset \mathsf{PGL}_2(\mathbb{R})$ to $\mathsf{PGL}_d(\mathbb{R})$ contains a unipotent element with a single Jordan block in its image, then it is necessarily a (cusped) Hitchin representation. We also show that the amalgamation of a Hitchin representation with a cusped Borel Anosov representation that is not Hitchin is never cusped Borel Anosov., Comment: 13 pages

Published
2023

12. Discrete Coxeter groups

Author

Lee, Gye-Seon and Marquis, Ludovic

Subjects
Mathematics - Geometric Topology, Mathematics - Group Theory, Mathematics - Metric Geometry, 20F55, 20F65, 20H10, 22E40, 51F15, 53C50, 57M50, 57S30
Abstract

Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This survey particularly focuses on how one uses Coxeter groups to construct interesting examples of discrete subgroups of Lie groups., Comment: 19 pages, 6 figures and 4 tables. To appear as a chapter of "Surveys in geometry"

Published
2021

13. Deformation spaces of Coxeter truncation polytopes

Author

Choi, Suhyoung, Lee, Gye-Seon, and Marquis, Ludovic

Subjects
Mathematics - Geometric Topology, Mathematics - Group Theory, 22E40, 20F55, 57M50, 57N16, 57S30
Abstract

A convex polytope $P$ in the real projective space with reflections in the facets of $P$ is a Coxeter polytope if the reflections generate a subgroup $\Gamma$ of the group of projective transformations so that the $\Gamma$-translates of the interior of $P$ are mutually disjoint. It follows from work of Vinberg that if $P$ is a Coxeter polytope, then the interior $\Omega$ of the $\Gamma$-orbit of $P$ is convex and $\Gamma$ acts properly discontinuously on $\Omega$. A Coxeter polytope $P$ is $2$-perfect if $P \smallsetminus \Omega$ consists of only some vertices of $P$. In this paper, we describe the deformation spaces of $2$-perfect Coxeter polytopes $P$ of dimension $d \geqslant 4$ with the same dihedral angles when the underlying polytope of $P$ is a truncation polytope, i.e. a polytope obtained from a simplex by successively truncating vertices. The deformation spaces of Coxeter truncation polytopes of dimension $d = 2$ and $d = 3$ were studied respectively by Goldman and the third author., Comment: 43 pages, 25 figures and tables. To appear in the Journal of the London Mathematical Society

Published
2021

21. Breastfeeding and impact on childhood hospital admissions: a nationwide birth cohort in South Korea

Author

Lee, Jeong-Seon, Shin, Jae Il, Kim, Sunyeup, Choi, Yong-Sung, Shin, Youn Ho, Hwang, Jimin, Shin, Jung U, Koyanagi, Ai, Jacob, Louis, Smith, Lee, Jeong, Han Eol, Noh, Yunha, Oh, In-Sun, Rhee, Sang Youl, Min, Chanyang, Cho, Seong Ho, Turner, Steve, Fond, Guillaume, Boyer, Laurent, Suh, Dong In, Acharya, Krishna Prasad, Shin, Ju-Young, Lee, Seung Won, and Yon, Dong Keon

Published
2023
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23. Lrig1-expression confers suppressive function to CD4+ cells and is essential for averting autoimmunity via the Smad2/3/Foxp3 axis

Author

Moon, Jae-Seung, Ho, Chun-Chang, Park, Jong-Hyun, Park, Kyungsoo, Shin, Bo-Young, Lee, Su-Hyeon, Sequeira, Ines, Mun, Chin Hee, Shin, Jin-Su, Kim, Jung-Ho, Kim, Beom Seok, Noh, Jin-Wook, Lee, Eui-Seon, Son, Ji Young, Kim, Yuna, lee, Yeji, Cho, Hee, So, SunHyeon, Park, Jiyoon, Choi, Eunsu, Oh, Jong-Won, Lee, Sang-Won, Morio, Tomohiro, Watt, Fiona M., Seong, Rho Hyun, and Lee, Sang-Kyou

Published
2023
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27. Anosov triangle reflection groups in SL(3,R)

Author

Lee, Gye-Seon, Lee, Jaejeong, and Stecker, Florian

Subjects
Mathematics - Geometric Topology, Mathematics - Group Theory, 22E40, 51F15, 57S30
Abstract

We identify all Anosov representations of compact hyperbolic triangle reflection groups into $\mathrm{SL}(3,\mathbb R)$. Specifically, we prove that such a representation is Anosov if and only if it lies in the Hitchin component of the representation space, or it lies in the Barbot component and the product of the three generators of the triangle group has distinct real eigenvalues., Comment: 42 pages, 11 figures

Published
2021

33. Convex cocompactness for Coxeter groups

Author

Danciger, Jeffrey, Guéritaud, François, Kassel, Fanny, Lee, Gye-Seon, and Marquis, Ludovic

Subjects
Mathematics - Group Theory, Mathematics - Geometric Topology
Abstract

We investigate representations of Coxeter groups into $\mathrm{GL}(n,\mathbb{R})$ as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mathbb{R}^n)$. We characterize which Coxeter groups admit such representations, and we fully describe the corresponding spaces of convex cocompact representations as reflection groups, in terms of the associated Cartan matrices. The Coxeter groups that appear include all infinite, word hyperbolic Coxeter groups; for such groups the representations as reflection groups that we describe are exactly the projective Anosov ones. We also obtain a large class of nonhyperbolic Coxeter groups, thus providing many examples for the theory of nonhyperbolic convex cocompact subgroups in $\mathbb{P}(\mathbb{R}^n)$ developed in arXiv:1704.08711., Comment: 60 pages, 8 figures. To appear in the Journal of the European Mathematical Society

Published
2021

34. A small closed convex projective 4-manifold via Dehn filling

Author

Lee, Gye-Seon, Marquis, Ludovic, and Riolo, Stefano

Subjects
Mathematics - Geometric Topology, 22E40, 53A20, 53C15, 57M50, 57N16, 57S30
Abstract

In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a cusped hyperbolic four-manifold through a continuous path of projective cone-manifolds., Comment: 29 pages, 8 figures. To appear in Publicacions Matem\`atiques

Published
2019
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45. Hitchin components for orbifolds

Author

Alessandrini, Daniele, Lee, Gye-Seon, and Schaffhauser, Florent

Subjects
Mathematics - Geometric Topology, Mathematics - Algebraic Geometry, Mathematics - Differential Geometry
Abstract

We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichm\"{u}ller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open ball and we compute its dimension explicitly. We then give applications to the study of the pressure metric, cyclic Higgs bundles, and the deformation theory of real projective structures on $3$-manifolds., Comment: 43 pages. v5: Final version, to appear in JEMS

Published
2018

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