Research

I am interested in low dimensional topology and hyperbolic geometry, and their interactions. I have worked on the following three topics: LERFness of 3-manifold groups, virtual properties of hyperbolic 3-manifolds, profinite completion of 3-manifold groups, non-zero degree maps between 3-manifolds, and pseudo-Anosov maps versus the topology of mapping tori.

Publications and preprints

    Published and accepted papers
  1. Joint with Zhongzi Wang, Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π_1, preprint 2021, accepted by Journal of Topology and Analysis.
  2. Virtual domination of 3-manifolds, III , Algebraic & Geometric Topology 25 (2025) 1599 - 1666.
  3. Joint with Nikolay Bogachev, Leone Slavich, Arithmetic trialitarian hyperbolic lattices are not LERF, (joint with Nikolay Bogachev, Leone Slavich), International Mathematics Research Notices, 2024(13), 10081 - 10087.
  4. Joint with Christoforos Neofytidis, Ye Tian, Shicheng Wang, Zhongzi Wang, On the realisation problem for mapping degree sets, Proceeding of the AMS, Volume 152, Number 4, 2024, 1769-1776.
  5. Joint with Zhongzi Wang, Minimal Euler characteristics of 4-manifolds with 3-manifold groups, Science China Mathematics, (2023), volume 66, pages 2325 - 2336.
  6. Virtual domination of 3-manifolds II , Journal of the London Mathematical Society, Volume 108, Issue 3, 2023, 869-915.
  7. All finitely generated 3-manifold groups are Grothendieck rigid, Groups Geom. Dyn. 17 (2023), no. 2, 385-402
  8. The panted cobordism group of cusped hyperbolic 3-manifolds, Journal of Topology, Volume 15 (2022), no.3, 1580-1634.
  9. Joint with Yi Liu, Toward and after virtual specialization in 3-manifold topology, Surveys in Differential Geometry, Vol. 25, No. 1 (2020), 215-252.
  10. Joint with Hoang Thanh Nguyen, Subgroup distortion of 3-manifold groups, Trans. Amer. Math. Soc, 373 (2020), no. 9, 6683-6711.
  11. A characterization on separable subgroups of 3-manifold groups, Journal of Topology 13 (2020), no.1, 187 236.
  12. Joint with Thomas Koberda and Feng Luo, An effective Lie--Kolchin theorem for quasi-unipotent matrices, Linear Algebra and its applications, Volume 581 (2019), 304-323.
  13. Geometrically finite amalgamations of hyperbolic 3-manifold groups are not LERF, Proc. Lond. Math. Soc., 118 (2019), no. 2, 257-283.
  14. Joint with Pierre Derbez, Yi Liu and Shicheng Wang, Volume of representations and mapping degree, Adv. Math., vol 351 (2019), 570-613.
  15. Non-LERFness of arithmetic hyperbolic manifold groups and mixed 3-manifold groups, Duke Math. J. 168 (2019), no.4, 655-696.
  16. Joint with Yi Liu, Virtual 1-domination of 3-manifolds, Compos. Math. 154 (2018), no. 3, 621 - 639.
  17. Virtual homological spectral radius and mapping torus of pseudo-Anosov maps, Proc. Amer. Math. Soc. 145 (2017), no. 10, 4551 4560.
  18. Joint with Pierre Derbez, Yi Liu and Shicheng Wang, Positive simplicial volume implies virtually positive Seifert volume for 3-manifolds, Geometry & Topology 21-5 (2017), 3159 - 3190.
  19. Virtual Domination of 3-manifolds, Geometry & Topology 19-4 (2015), 2277 - 2328.
  20. Virtual Homological Torsion of Closed Hyperbolic 3-manifolds, J. Differential Geom. 100 (2015), no. 3, 547 - 583.
  21. A Transcendental Invariant of Pseudo-Anosov Maps, J. Topology (2015) 8 (3), 711-743.
  22. Joint with Yi Liu, Yi Ni, and Shicheng Wang, On slope genera of knotted tori in 4-space, Pacific J. Math. 261 (2013), no. 1, 117 - 144
  23. Joint with Shicheng Wang, Jianchun Wu and Hao Zheng, Self-mapping degrees of 3-manifolds, Osaka J.Math 49 (2013), no. 1, 247 - 269
  24. Joint with Danny Calegari and Shicheng Wang, On fibered commensurability, Pacific J. Math 250 (2011), no. 2, 287 - 317
  25. Joint with Pierre Derbez and Shicheng Wang, Finiteness of mapping degree sets for 3-manifolds, Acta Math. Sin. (Engl. Ser.) 27 (2011), no. 5, 807 - 812
  26. Joint with Shicheng Wang and Jianchun Wu, Self-mapping degrees of torus bundles and torus semi-bundles, Osaka J. Math. 47 (2010), no. 1, 131 - 155
  27. Degree ±1 self-maps and self-homeomorphisms on prime 3-manifolds, Algebr. Geom. Topol. 10 (2010), no. 2, 867 - 890
    Preprints:
  1. Joint with Christoforos Neofytidis, Ye Tian, Shicheng Wang, Zhongzi Wang, Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets, preprint 2025.
  2. Joint with Zhongzi Wang, On virtual chirality of 3-manifolds , preprint 2025.
  3. Joint with Inkang Kim, On the degree of a finite cover which fibers over circle , preprint 2021.