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.
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.
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.