# 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. Paper

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. Summary

We prove that non-virtually-free mapping class groups never admit, even virtually, any 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.

We prove that every right-angled Artin group 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). Summary

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 show that the converse is not true for each surface S with 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 Summary

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.

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

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.

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.

We prove that the double of a rank-two free group either splits as a 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.

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

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

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

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

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

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

## Preprint

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

We prove that if G is non-virtually-metabelian, then (G x Z) * Z never admits an embedding into the C2 diffeomorphism group of a compact one-manifold. As a consequence, we completely classify RAAGs that embed into Diffr(S1) for 2 ≤ r ≤ infinity.

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 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.