Up: Jon McCammond's Home Page
Publications and Preprints
- The word problem for Burnside semigroups: a positive solution
for a ≥ 6, Dissertation, University of California,
- 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.
- Gaps in Categories in Monoids and Semigroups with
Applications (J. Rhodes, editor), World Scientific, Singapore,
- Gaps between connected finite graphs (with
R. Baldinger), International
Journal of Algebra and Computation 2 (1992), 19-32.
Gaps in the categories of finite directed and finite transitive
R. Baldinger) International
Journal of Algebra and Computation 8 (1998), no. 1, 35-60.
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.
- Integrating Polynomials in Secant and Tangent
Mathematical Monthly 106 (1999), no. 9, 856-858.
General small cancellation theory, International
Journal of Algebra and Computation. 10 (2000), no. 1,
1-172. pdf. Also available in sections.
Three-generator Artin groups of large type are biautomatic
(with T. Brady)
J. of Pure and Applied
Algebra, 151 (2000), 1-9.
- Normal forms for free aperiodic semigroups, International
Journal of Algebra and Computation 11 (2001), no. 5,
- 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.
Fans and ladders in small cancellation theory, (with D. Wise) Proceedings of
the LMS 84 (2002), no. 3, 599-644.
- Curvature testing in 3-dimensional metric polyhedral complexes,
(with M. Elder) Experimental Mathematics 11
(2002), no. 1, 143-158.
- Rigidity of Coxeter groups and Artin groups (with N. Brady,
B. Muehlherr, and W. Neumann)
94 (2002), no. 1, 91-109.
- Combinatorial conditions that imply word-hyperbolicity for
3-manifolds (with M. Elder and
(2003), no. 6, 1241-1259.
- 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.
- Bounding edge degrees in triangulated 3-manifolds (with N. Brady and
Proceedings of the AMS
132 (2004), no. 1, 291-298.
- The hypertree poset and the l2-Betti numbers of the
motion group of the trivial link
(with J. Meier)
Annalen 328 (2004), no. 4, 633-652.
- CAT(0) is algorithmic, (with M. Elder)
Dedicata 107 (2004), no. 1, 25-46.
- Coherence, local quasiconvexity, and the perimeter of
2-complexes, (with D. Wise) GAFA
15 (2005), 859-927.
- Non-commutative Groebner bases for the commutator ideal, (with
Journal of Algebra and Computation 16 (2006), 187-202.
- Noncrossing partitions in surprising locations. American Mathematical
Monthly 113 (2006) 598-610. (AMM version)
- The length spectrum of a compact constant curvature complex is
N. Brady) Geometriae
Dedicata 119 (2006) 159-167.
- The integral cohomology of the group of loops (with C. Jensen and
Geometry and Topology
10 (2006), 759-784.
- h-vectors of generalized associahedra and noncrossing partitions
T. Brady and
Mathematics Research Notices (2006), Article ID 69705,
- 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.
- Locally quasiconvex small cancellation groups (with
Transactions of the AMS
360 (2008), 237-271.
- Order independence in asynchronous cellular automata (with M. Macauley and
Cellular Automata 3 (2008), 37-56.
- Constructing non-positively curved spaces and groups
and cohomological methods in group theory, LMS Lecture Note
Series 358 (2009), 162--224. Survey
- Geometric presentations for pure braid group (with Dan Margalit)
Journal of Knot
Theory and Its Ramifications 18 (2009) 1-20.
- Braids, posets and orthoschemes
(with T. Brady)
Geometric Topology 10 (2010), 2277-2314.
- Windmills and extreme 2-cells
(with D. Wise) Illinois
Journal of Mathematics 54 (2011), 69-87.
- Combinatorial descriptions of multi-vertex
Journal of Mathematics 54 (2011), 137-154.
- Dynamics groups of asynchronous cellular automata (with M. Macauley and
Journal of Algebraic Combinatorics 33 (2011), 11-35.
- Bounding reflection length in an affine Coxeter group (with T. Kyle Petersen)
Journal of Algebraic Combinatorics 34 (2011) 711-719.
- Triangles, squares and geodesics
(with R. Levitt)
Journal of Algebra and Computation 22 (2012), 34 pages.
- Artin groups of euclidean type (with
R. Sulway) Mathematisches
Forschungsinstitut Oberwolfach Report 49 (2012) 2964-2966.
- Factoring euclidean isometries
(with N. Brady)
Journal of Algebra and Computation 25 (2015), 325-347.
- Dual euclidean Artin groups and the failure of the lattice
of Algebra 437 (2015), 308-343.
- The BNS-invariant for the pure braid groups (with N. Koban and
geometry and dynamics 9 (2015), 665-682.
- Braid groups and euclidean simplices (with E. Leyton Chisholm)
in Configuration Spaces:Geometry, Topology and Representation
theory, Springer-INDAM series (2016), 291-311.
- 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)
- Artin groups of euclidean type (with
R. Sulway) Inventiones
Mathematicae (2017), 1-52 (online version).
- Undesired parking spaces and contractible pieces of the
noncrossing partition link, (with Michael
Journal of Combinatorics (2018),
1-13. pdf arx
- Computing reflection length in an affine Coxeter group
(with Joel Lewis,
Kyle Petersen and Petra Schwer), to appear in the Transactions of the AMS
- The mysterious geometry of Artin groups (survey article to
appear in Winter Braids Lecture Notes)
(44 pages) pdf
- Boundary braids, (with Michael Dougherty and Stefan Witzel)
arx (49 pages)
- Fixed points of parking functions, (with Hugh Thomas and
Nathan Williams), pdf
arx (37 pages)
- Tits alternative for groups acting properly on 2-dimensional
(3 page appendix, with Damian Osajda and Piotr Przytycki) pdf
- Connectivity at infinity for the braid group of a complete
bipartite graph, (with Kristen Mazur, John Meier and Ranjan Rohatgi)
arx (23 pages)
- Noncrossing hypertrees,
arx (53 pages)
- A complex euclidean reflection group with an elegant complement
complex, (with Ben Cote) pdf
arx (30 pages)
- Critical points, critical values, and a determinant identity
for complex polynomials (with Michael
Dougherty) pdf (14 pages)
- Geometric semigroup theory, (with J. Rhodes and B. Steinberg)
(66 pages) pdf
- The infinite cyclohedron and its automorphism group, (with
A. Fossas Tenas) (18 pages)
- Curvature and computation (expository) (10 pages)
- The exceptional symmetry (short note) (8
- An introduction to Garside structures (28 pages)
- The 0/1-Borsuk conjecture is generically true for each fixed
diameter, (with G. Ziegler)
unpublished (8 pages)
Here are some slides from a mini-course I gave in Regensburg in September
2017: Talk 1
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