# Publications (Sang-hyun Kim)

## 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 C1+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(S2) by a quasi-isometry with word-- or Lp--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 S2 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 {Gi}, we study the kernel K of the map G -> ∏i Gi. We show K embeds into some RAAG. When each Gi 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 C1+bv diffeomorphism group of a compact one-manifold. As a consequence, we have a complete classification of RAAGs that embed into Diffr(S1) 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.

## Publication: related area

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.