# Publications (Sang-hyun Kim)

Publications by Sang-hyun Kim can be downloaded at http://arxiv.org/a/kim_s_3.

## Contents

## Published / to appear

15. (With Cheol-Hyun Cho, Hansol Hong and Siu-Cheong Lau), Lagrangian Floer potential of orbifold spheres, Advances in Mathematics Volume 306, 14 January 2017, Pages 344-426. Published

- We compute Lagrangian Floer potentials for Seidel Lagrangians on hyperbolic 2--orbifold spheres.

14. (With Hyungryul Baik and Thomas Koberda), Unsmoothable group actions on compact one-manifolds, accepted, Journal of European Mathematical Society.

- Let G be the mapping class group of a surface (possibly with punctures or boundary), such that G is not virtually free. We prove that G
*never*admits, even virtually, an embedding into the C^{1+bv}diffeomorphism group of the circle.

13. (With Hyungryul Baik and Thomas Koberda), Right-angled Artin subgroups of the C^{∞} interval diffeomorphism group, June 2016, Volume 213, Issue 1, pp 175-182, Israel Journal of Mathematics. Published

- We prove that every RAAG embeds into the C
^{∞}diffeomorphism group of the real line.

12. (With Thomas Koberda), Right-angled Artin groups and finite subgraphs of curve graphs, Vol. 53 No.3, Osaka Journal of Mathematics (2016).

- Let S be a surface with the complexity xi(S) < 3. We prove that if a RAAG A(X) embeds into Mod(S), then X must appear in the curve graph C(S) as an induced subgraph. We also give counterexamples for xi(S)>3.

11. (With Thomas Koberda), Anti-trees and right-angled Artin subgroups of braid groups, Geometry & Topology 19-6 (2015), 3289--3306. DOI 10.2140/gt.2015.19.3289 Published

- We prove that every RAAG (right-angled Artin group) embeds into some RAAG defined by an anti-tree. As a consequence, every RAAG embeds into some braid group, and also into Symp(S
^{2}) by a quasi-isometry with word-- or L^{p}--metric for p>2; this strengthens M. Kapovich's result.

10. (With Genevieve Walsh), Coxeter groups, hyperbolic cubes, and acute triangulations, Journal of Topology (2016) 9 (1): 117-142. doi: 10.1112/jtopol/jtv038 Published

- We prove that a combinatorial triangulation L of S
^{2}can be realized as an acute geodesic triangulation if and only if L does not have a separating three- or four-cycle.

9. (With Thomas Koberda), The geometry of the curve complex of a right-angled Artin group, International Journal of Algebra and Computation (2014) 24 (2) 121-169. Published

- We develop a theory of right-angled Artin group actions on extension graphs, which parallels mapping class group actions on curve graphs. In particular, we concretely compute an acylindricity constant of the action.

8. (With Sang-il Oum), Hyperbolic Surface subgroups of one-ended doubles of free groups, Journal of Topology (2014) 7 (4): 927--947. Published

- We prove that the double of a rank-two free group either splits as a nontrivial free product or contains a closed hyperbolic surface subgroup.

7. (With Thomas Koberda), An obstruction to embedding right-angled Artin groups in mapping class groups, International Mathematics Research Notices (2014) #2014 (14): 3912--3918. Published

- We prove that a large chromatic number of the defning graph is an obstruction for a RAAG to embed into a given mapping class group.

6. (With Thomas Koberda), Embedability between right-angled Artin groups, Geometry & Topology 17 (2013) 493--530. Published

- We propose that a notion of ``extension graph
*can be used for a systematic study of embedability between two RAAGs.*

5. (With Henry Wilton), Polygonal words in free groups, Quarterly Journal of Mathematics (2012) 63(2), 399--421. Published

- We define a combinatorial group theoretic notion ``polygonality
*, and show that this notion can be used to find surface subgroups in many (conjecturally, all) doubles of free groups.*

4. Surface subgroups of graph products of groups, International Journal of Algebra and Computation (2012) 22 (8). Published

- For a graph product G of groups {G
_{i}}, we study the kernel K of the map G -> ∏_{i}G_{i}. We show K embeds into some RAAG. When each G_{i}is finite or cyclic, then G is virtually special. We deduce that when X is a graph with up to seven vertices, then the right-angled Coxeter groups on X contains a hyperbolic surface subgroup if and only if X is weakly chordal.

3. Geometricity and polygonality in free groups, International Journal of Algebra and Computation 21(1--2) (2011) 235--256. Published

- We prove that ``geometric
*words (defined by Gordon--Wilton) are polygonal, as defined in [5].*

2. On right-angled Artin groups without surface subgroups, Groups, Geometry, and Dynamics 4(2) (2010) 275--307. Published

- We prove a combination theorem for the family of RAAGs that do not admit ``relative
*embedding of surface groups.*

1. Co-contractions of graphs and right-angled Artin groups, Algebraic and Geometric Topology 8 (2008) 849--868. Published

- We prove the injectivity of a map between RAAGs, which comes from a graph operation called ``co-contraction
*. A family of words that yield such embeddings, called ``contraction words*, is also described.

## Preprint

3. (With Thomas Koberda), Free products and algebraic structures of diffeomorphism groups, preprint.

- We prove that if a finitely generated group G is not virtually abelian, then (G x Z) * Z never admits an embedding into the C
^{1+bv}diffeomorphism group of a compact one-manifold. As a consequence, we have a complete classification of RAAGs that embed into Diff^{r}(S^{1}) for each 0 ≤ r ≤ ω. (The cases r ≤ 1 and r = ω were previously known)

2. (With Thomas Koberda and Yash Lodha), Chain groups of homeomorphisms of the interval and the circle, preprint.

- We study subgroups of Homeo(R) generated by finitely many homeomorphisms supported on single intervals. In particular, we construct uncountably many non-pairwise isomorphic countable simple orderable groups.

1. (With Thomas Koberda and Mahan Mj), Rotation spectra and exotic group actions on the circle, preprint.

- We study which finitely generated groups admit uncountably many pairwise-non-conjugate embeddings into PSL(2,R). In particular, we obtain a combination theorem of such a class of groups, encompassing free product and HNN extensions, both amalgamated over maximal abelian subgroups.

## Conference proceedings / surveys / other writings

1. (With Thomas Koberda and Juyoung Lee), Finite subgraphs of extension graphs.

- A strengthening and also a very detailed proof of Lemma 3.1 that originally appeared in
*Embedability between right-angled Artin groups*, Geometry & Topology 17 (2013) 493--530.

2. Chan-Byoung Chae, Sang-hyun Kim (2nd author) and Robert W. Heath Jr., Linear network coordinated beamforming for cell-boundary users, Proc. of IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC), June 21-24, 2009 (Perugia, Italy) (2009).

1. Chan-Byoung Chae, Sang-hyun Kim (2nd author) and Robert W. Heath Jr., Network coordinated beamforming for cell-boundary users: linear and non-linear approaches, IEEE Journal of Selected Topics in Signal Processing (J-STSP), Special Issue on Managing Complexity in Multiuser MIMO Systems, vol. 3, no. 6 (2009) 1094--1105.