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Publications and Preprints

arxiv / cv / msn / slides / ucsb


  1. The word problem for Burnside semigroups: a positive solution for a ≥ 6, Dissertation, University of California, Berkeley, 1991.
  2. The solution to the word problem for the relatively free semigroups satisfying Ta = Ta+b with a ≥ 6, International Journal of Algebra and Computation 1 (1991), 1-32.
  3. Gaps in Categories in Monoids and Semigroups with Applications (J. Rhodes, editor), World Scientific, Singapore, 1991, 83-85.
  4. Gaps between connected finite graphs (with R. Baldinger), International Journal of Algebra and Computation 2 (1992), 19-32.
  5. Gaps in the categories of finite directed and finite transitive graphs (with R. Baldinger) International Journal of Algebra and Computation 8 (1998), no. 1, 35-60. pdf
  6. Burnside groups and small cancellation theory Groups St. Andrews 1997 in Bath, II, 538--559, London Math. Soc. Lecture Note Ser., 261, Cambridge Univ. Press, Cambridge, 1999. pdf arx
  7. Integrating Polynomials in Secant and Tangent American Mathematical Monthly 106 (1999), no. 9, 856-858. pdf
  8. General small cancellation theory, International Journal of Algebra and Computation. 10 (2000), no. 1, 1-172. pdf. Also available in sections.
  9. Three-generator Artin groups of large type are biautomatic (with T. Brady) J. of Pure and Applied Algebra, 151 (2000), 1-9. pdf arx
  10. Normal forms for free aperiodic semigroups, International Journal of Algebra and Computation 11 (2001), no. 5, 581-625. pdf
  11. The pure symmetric automorphisms of a free group form a duality group (with N. Brady, J. Meier, and A. Miller) Journal of Algebra 246 (2001), no. 2, 881-896. pdf
  12. Fans and ladders in small cancellation theory, (with D. Wise) Proceedings of the LMS 84 (2002), no. 3, 599-644. pdf
  13. Curvature testing in 3-dimensional metric polyhedral complexes, (with M. Elder) Experimental Mathematics 11 (2002), no. 1, 143-158. pdf
  14. Rigidity of Coxeter groups and Artin groups (with N. Brady, B. Muehlherr, and W. Neumann) Geometriae Dedicata 94 (2002), no. 1, 91-109. pdf
  15. Combinatorial conditions that imply word-hyperbolicity for 3-manifolds (with M. Elder and J. Meier) Topology 42 (2003), no. 6, 1241-1259. pdf arx
  16. Local-to-asymptotic topology for cocompact CAT(0) complexes (with N. Brady and J. Meier) Topology and its Applications 131 (2003), no. 2, 177-188. pdf
  17. Bounding edge degrees in triangulated 3-manifolds (with N. Brady and J. Meier) Proceedings of the AMS 132 (2004), no. 1, 291-298. pdf
  18. The hypertree poset and the l2-Betti numbers of the motion group of the trivial link (with J. Meier) Mathematische Annalen 328 (2004), no. 4, 633-652. pdf
  19. CAT(0) is algorithmic, (with M. Elder) Geometriae Dedicata 107 (2004), no. 1, 25-46. pdf arx
  20. Coherence, local quasiconvexity, and the perimeter of 2-complexes, (with D. Wise) GAFA 15 (2005), 859-927. pdf arx
  21. Non-commutative Groebner bases for the commutator ideal, (with S. Hermiller) International Journal of Algebra and Computation 16 (2006), 187-202. pdf
  22. Noncrossing partitions in surprising locations. American Mathematical Monthly 113 (2006) 598-610. (AMM version) pdf arx
  23. The length spectrum of a compact constant curvature complex is discrete (with N. Brady) Geometriae Dedicata 119 (2006) 159-167. pdf
  24. The integral cohomology of the group of loops (with C. Jensen and J. Meier) Geometry and Topology 10 (2006), 759-784. pdf
  25. h-vectors of generalized associahedra and noncrossing partitions (with C. Athanasiadis, T. Brady and C. Watt) International Mathematics Research Notices (2006), Article ID 69705, 1-28. (electronic) pdf arx
  26. The Euler characteristic of the Whitehead automorphism group of a free product (with C. Jensen and J. Meier) Transactions of the AMS 359 (2007), 2577-2595. pdf arx
  27. Locally quasiconvex small cancellation groups (with D. Wise) Transactions of the AMS 360 (2008), 237-271. pdf
  28. Order independence in asynchronous cellular automata (with M. Macauley and H. Mortveit) Journal of Cellular Automata 3 (2008), 37-56. pdf arx
  29. Constructing non-positively curved spaces and groups in Geometeric and cohomological methods in group theory, LMS Lecture Note Series 358 (2009), 162--224. Survey article. pdf
  30. Geometric presentations for pure braid group (with Dan Margalit) Journal of Knot Theory and Its Ramifications 18 (2009) 1-20. pdf arx
  31. Braids, posets and orthoschemes (with T. Brady) Algebraic and Geometric Topology 10 (2010), 2277-2314. pdf arx
  32. Windmills and extreme 2-cells (with D. Wise) Illinois Journal of Mathematics 54 (2011), 69-87. pdf arx
  33. Combinatorial descriptions of multi-vertex 2-complexes Illinois Journal of Mathematics 54 (2011), 137-154. pdf arx
  34. Dynamics groups of asynchronous cellular automata (with M. Macauley and H. Mortveit) Journal of Algebraic Combinatorics 33 (2011), 11-35. pdf arx
  35. Bounding reflection length in an affine Coxeter group (with T. Kyle Petersen) Journal of Algebraic Combinatorics 34 (2011) 711-719. pdf arx
  36. Triangles, squares and geodesics (with R. Levitt) International Journal of Algebra and Computation 22 (2012), 34 pages. pdf arx
  37. Artin groups of euclidean type (with R. Sulway) Mathematisches Forschungsinstitut Oberwolfach Report 49 (2012) 2964-2966. pdf
  38. Factoring euclidean isometries (with N. Brady) International Journal of Algebra and Computation 25 (2015), 325-347. pdf arx
  39. Dual euclidean Artin groups and the failure of the lattice property Journal of Algebra 437 (2015), 308-343. pdf arx
  40. The BNS-invariant for the pure braid groups (with N. Koban and J. Meier) Groups, geometry and dynamics 9 (2015), 665-682. pdf arx
  41. Braid groups and euclidean simplices (with E. Leyton Chisholm) in Configuration Spaces:Geometry, Topology and Representation theory, Springer-INDAM series (2016), 291-311. pdf arx
  42. The structure of euclidean Artin groups, Geometric and cohomological group theory (London Mathematical Society Lecture Note Series), Kropholler, P., Leary, I., Martinez, C., & Nucinkis, B. (Eds.). Cambridge University Press, (2017), 82-114. (survey article) pdf arx
  43. Artin groups of euclidean type (with R. Sulway) Inventiones Mathematicae (2017), 1-52 (online version). pdf arx
  44. The mysterious geometry of Artin groups, in Winter Braids Lecture Notes, 4 (2017), 1--30. pdf wbln (survey article)
  45. Undesired parking spaces and contractible pieces of the noncrossing partition link, (with Michael Dougherty) Electronic Journal of Combinatorics (2018), 1-13. pdf arx
  46. Computing reflection length in an affine Coxeter group (with Joel Lewis, Kyle Petersen and Petra Schwer), Proceedings of the 30th International Conference on Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire, 80B.51 (2018), 12 pp. pdf (extended abstract)
  47. Computing reflection length in an affine Coxeter group (with Joel Lewis, Kyle Petersen and Petra Schwer), Transactions of the AMS, 371, (2019), 4097--4127. pdf arx
  48. Boundary braids, (with Michael Dougherty and Stefan Witzel), Algebraic & Geometric Topology 20-7 (2020), 3505--3560. pdf arx
  49. Critical points, critical values, and a determinant identity for complex polynomials (with Michael Dougherty), Proceedings of the AMS 148 (2020), 5277-5289. pdf
  50. A complex euclidean reflection group with a non-positively curved complement complex, (with Ben Coté), Groups, Geometry and Dynamics 15 (2021), 989-1013. pdf arx
  51. Tits alternative for groups acting properly on 2-dimensional recurrent complexes, (with Damian Osajda and Piotr Przytycki), Advances in Mathematics 391 (2021). pdf arx (3 page appendix)
to appear
  1. Geometric combinatorics of polynomials I: the case of a single polynomial (with Michael Dougherty), to appear in the Journal of Algebra arx (30 pages)
  2. Connectivity at infinity for the braid group of a complete bipartite graph, (with Kristen Mazur, John Meier and Ranjan Rohatgi), to appear in the Rocky Mountain Journal of Mathematics pdf arx (23 pages)
  3. Factoring isometries of quadratic spaces into reflections, (with Giovanni Paolini), to appear in the Journal of Algebra arx (30 pages)
  1. Fixed points of parking functions, (with Hugh Thomas and Nathan Williams), pdf arx (37 pages)
  2. Dual braids and the braid arrangement (survey) pdf (15 pages)
software other writings

Here are some slides from a mini-course I gave in Regensburg in September 2017: Talk 1 Exercises Talk 2 Talk 3
During the course I claimed that braid groups are CAT(0). Unfortunately, we have found a mistake, so we have had to retract our claim.

Last modified 11/May/2015 by jon.mccammond@math.ucsb.edu