Preprints


  1. Cofinal elements and fractional Dehn twist coefficients (with Ty Ghaswala) in preparation.

  2. Order-detection of slopes on the boundaries of knot manifolds (with Steve Boyer) 26 pages, submitted. ArXiv link

  3. The number of locally invariant orderings of a group (with Idrissa Ba and Ian Thompson) 13 pages, submitted. ArXiv link

  4. Graph manifolds that admit arbitrarily many Anosov flows (with Tali Pinsky) 20 pages, submitted. ArXiv link

  5. Circular orderability of 3-manifold groups (with Idrissa Ba) 33 pages, submitted. ArXiv link



Research Publications


  1. A theorem of Mumford and Ramanujam for universal algebras (with R. Padmanabhan) Algebra Universalis (83) Article number:38 (2022). Journal link

  2. Borel structures on the space of left-orderings (with Filippo Calderoni) Bulletin of the London Mathematical Society (54) 1 (2022) 83-94. Journal link, ArXiv link.

  3. Circularly ordering direct products and the obstruction to left-orderability (with Ty Ghaswala), Pacific Journal of Mathematics (312) 2 (2021) 401–419. Journal link, ArXiv link.

  4. The space of circular orderings and semiconjugacy (with Idrissa Ba) Journal of Algebra (15) 586 (2021), 582-606. Journal Link , ArXiv link.

  5. Promoting circular-orderability to left-orderability (with Jason Bell and Ty Ghaswala) Annales de l'Institut Fourier (1) 71 (2021), 175-201. Journal Link , ArXiv link.

  6. Generalizations of the Burns-Hale theorem Communications in Algebra,(11) 48 (2020), 4846-4858. Journal Link , ArXiv link.

  7. Dense orderings in the space of left-orderings of a group (with Tessa Reimer) Canadian Mathematical Bulletin (2) 63 (2020), 393-404. Journal Link , ArXiv link.

  8. Free products of circularly ordered groups with amalgamated subgroup (with Ty Ghaswala) Journal of the London Mathematical Society (3) 100 (2019), 775-803 Journal Link , ArXiv link.

  9. On the number of circular orders on a group (with Cristóbal Rivas and Kathryn Mann) Journal of Algebra 504 (2018) 336-363. Journal link, ArXiv link.

  10. Foliations, orders, representations, L-spaces and graph manifolds (with Steve Boyer) Adv. Math. 310 (2017), 159-234. Journal link, ArXiv link.

  11. Automorphisms acting on the left-orderings of a bi-orderable group (with Sina Zabanfahm) New York Journal of Mathematics 23 (2017), 159-234. Journal link, ArXiv link.

  12. Ordered Groups and Topology (book with Dale Rolfsen) Graduate Studies in Mathematics. American Mathematical Society, Providence RI, 2016. Publisher link, ArXiv link.

  13. Testing bi-orderability of knot groups (with Colin Desmarais and Patrick Naylor) Canadian Mathematical Bulletin 59 (2016), 472-482. Journal link, ArXiv link.

  14. Left-orderability and exceptional Dehn surgery on two-bridge knots (with Masakazu Teragaito). Contemporary Mathematics, proceedings of the conference Geometry and Topology down under, 597 (2013) 225--233. ArXiv link

  15. Graph manifolds, left-orderability and amalgamation (with Liam Watson and Tye Lidman) Algebraic & Geometric Topology 13 (2013), 2347–2368. Journal link, ArXiv link

  16. Left-orderings and quotients of the braid groups, J. Knot Theory Ramifications, 21, (2012) 9 pages. Journal link

  17. Left-orderable fundamental groups and Dehn surgery, (with Liam Watson). International Mathematics Research Notices, (2012) 29 pages. Journal link, ArXiv link

  18. Ordered groups, eigenvalues, knots, surgery and L-spaces, (with Dale Rolfsen). Math. Proc. Camb. Phil. Soc. (2012), 152, 115--129. Journal link, ArXiv link

  19. Free lattice-ordered groups and the space of left-orderings. Monatshefte für Mathematik (2012), 167(3-4), pp 417-430. Journal link

  20. On cabled knots, Dehn surgery, and left-orderable fundamental groups (with Liam Watson). Math. Res. Lett. 18 (2011), no. 06, 1085–1095. Journal link , ArXiv link

  21. Exotic left orderings of the free groups from the Dehornoy ordering. Bull. Aust. Math. Soc. 84 (2011), 103–110 Journal link, ArXiv link

  22. Isolated points in the space of left orderings of a group, Groups, Geometry and Dynamics Volume 4, Issue 3, 2010, pp. 517-532. Journal link, ArXiv link

  23. A new characterization of Conrad's property for group orderings, with applications (By Andrès Navas and Cristóbal Rivas, my contribution is the Appendix), Algebraic & Geometric Topology 9 (2009) 2079-2100. Journal link, ArXiv link

  24. Corrigendum to "On ordering free groups" [J. Symbolic Comput. 40 (2005) 1285-1290] (with Lawrence H. Smith), Journal of Symbolic Computation, Vol. 44, No. 10, October 2009, 1529-1532. Journal link

  25. Densely ordered braid subgroups (with Dale Rolfsen), Journal of Knot Theory and its Ramifications, Vol. 16 No. 7 869-877. Journal link, ArXiv link

Unpublished and expository work


  1. Left-orderability of 3-manifold fundamental groups (invited expository piece) CMS Notes 48 (2016) no. 2, 14-15. Publisher link.

  2. Slope detection, foliations in graph manifolds, and L-spaces (with Steve Boyer, 2015) ArXiv link.

  3. Non-bi-orderability of knot groups from Dehn’s presentation(with Colin Desmarais)

  4. Orderable groups and topology minicourse, (notes from Santiago 2014 orderable groups workshop)

  5. Ordered groups and bundles (with Mathieu Anel, 2012) ArXiv link.