Up: Jon McCammond's Home Page
Publications and Preprints
arxiv /
cv /
msn /
slides /
ucsb
published
 The word problem for Burnside semigroups: a positive solution
for a ≥ 6, Dissertation, University of California,
Berkeley, 1991.
 The solution to the word problem for the relatively free
semigroups satisfying T^{a} = T^{a+b} with a
≥ 6, International Journal of Algebra and
Computation 1 (1991), 132.
 Gaps in Categories in Monoids and Semigroups with
Applications (J. Rhodes, editor), World Scientific, Singapore,
1991, 8385.
 Gaps between connected finite graphs (with
R. Baldinger), International
Journal of Algebra and Computation 2 (1992), 1932.

Gaps in the categories of finite directed and finite transitive
graphs (with
R. Baldinger) International
Journal of Algebra and Computation 8 (1998), no. 1, 3560.
pdf

Burnside groups and small cancellation theory Groups
St. Andrews 1997 in Bath, II, 538559, London Math. Soc. Lecture
Note Ser., 261, Cambridge Univ. Press, Cambridge, 1999.
pdf
arx
 Integrating Polynomials in Secant and Tangent
American
Mathematical Monthly 106 (1999), no. 9, 856858.
pdf

General small cancellation theory, International
Journal of Algebra and Computation. 10 (2000), no. 1,
1172. pdf. Also available in sections.

Threegenerator Artin groups of large type are biautomatic
(with T. Brady)
J. of Pure and Applied
Algebra, 151 (2000), 19.
pdf
arx
 Normal forms for free aperiodic semigroups, International
Journal of Algebra and Computation 11 (2001), no. 5,
581625.
pdf
 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, 881896.
pdf

Fans and ladders in small cancellation theory, (with D. Wise) Proceedings of
the LMS 84 (2002), no. 3, 599644.
pdf
 Curvature testing in 3dimensional metric polyhedral complexes,
(with M. Elder) Experimental Mathematics 11
(2002), no. 1, 143158.
pdf
 Rigidity of Coxeter groups and Artin groups (with N. Brady,
B. Muehlherr, and W. Neumann)
Geometriae
Dedicata
94 (2002), no. 1, 91109.
pdf
 Combinatorial conditions that imply wordhyperbolicity for
3manifolds (with M. Elder and
J. Meier)
Topology 42
(2003), no. 6, 12411259.
pdf
arx
 Localtoasymptotic topology for cocompact CAT(0) complexes
(with N. Brady and
J. Meier) Topology and its
Applications 131 (2003), no. 2, 177188.
pdf
 Bounding edge degrees in triangulated 3manifolds (with N. Brady and
J. Meier)
Proceedings of the AMS
132 (2004), no. 1, 291298.
pdf
 The hypertree poset and the l^{2}Betti numbers of the
motion group of the trivial link
(with J. Meier)
Mathematische
Annalen 328 (2004), no. 4, 633652.
pdf
 CAT(0) is algorithmic, (with M. Elder)
Geometriae
Dedicata 107 (2004), no. 1, 2546.
pdf
arx
 Coherence, local quasiconvexity, and the perimeter of
2complexes, (with D. Wise) GAFA
15 (2005), 859927.
pdf
arx
 Noncommutative Groebner bases for the commutator ideal, (with
S. Hermiller)
International
Journal of Algebra and Computation 16 (2006), 187202.
pdf
 Noncrossing partitions in surprising locations. American Mathematical
Monthly 113 (2006) 598610. (AMM version)
pdf
arx
 The length spectrum of a compact constant curvature complex is
discrete (with
N. Brady) Geometriae
Dedicata 119 (2006) 159167.
pdf
 The integral cohomology of the group of loops (with C. Jensen and
J. Meier)
Geometry and Topology
10 (2006), 759784.
pdf
 hvectors of generalized associahedra and noncrossing partitions
(with
C. Athanasiadis,
T. Brady and
C.
Watt) International
Mathematics Research Notices (2006), Article ID 69705,
128. (electronic)
pdf
arx
 The Euler characteristic of the Whitehead automorphism group of
a free product
(with C. Jensen
and J. Meier) Transactions
of the AMS
359 (2007), 25772595.
pdf
arx
 Locally quasiconvex small cancellation groups (with
D. Wise)
Transactions of the AMS
360 (2008), 237271.
pdf
 Order independence in asynchronous cellular automata (with M. Macauley and
H. Mortveit)
Journal of
Cellular Automata 3 (2008), 3756.
pdf
arx
 Constructing nonpositively curved spaces and groups
in Geometeric
and cohomological methods in group theory, LMS Lecture Note
Series 358 (2009), 162224. Survey
article.
pdf
 Geometric presentations for pure braid group (with Dan Margalit)
Journal of Knot
Theory and Its Ramifications 18 (2009) 120.
pdf
arx
 Braids, posets and orthoschemes
(with T. Brady)
Algebraic and
Geometric Topology 10 (2010), 22772314.
pdf
arx
 Windmills and extreme 2cells
(with D. Wise) Illinois
Journal of Mathematics 54 (2011), 6987.
pdf
arx
 Combinatorial descriptions of multivertex
2complexes Illinois
Journal of Mathematics 54 (2011), 137154.
pdf
arx
 Dynamics groups of asynchronous cellular automata (with M. Macauley and
H. Mortveit)
Journal of Algebraic Combinatorics 33 (2011), 1135.
pdf
arx
 Bounding reflection length in an affine Coxeter group (with T. Kyle Petersen)
Journal of Algebraic Combinatorics 34 (2011) 711719.
pdf
arx
 Triangles, squares and geodesics
(with R. Levitt)
International
Journal of Algebra and Computation 22 (2012), 34 pages.
pdf
arx
 Artin groups of euclidean type (with
R. Sulway) Mathematisches
Forschungsinstitut Oberwolfach Report 49 (2012) 29642966.
pdf
 Factoring euclidean isometries
(with N. Brady)
International
Journal of Algebra and Computation 25 (2015), 325347.
pdf
arx
 Dual euclidean Artin groups and the failure of the lattice
property Journal
of Algebra 437 (2015), 308343.
pdf
arx
 The BNSinvariant for the pure braid groups (with N. Koban and
J. Meier)
Groups,
geometry and dynamics 9 (2015), 665682.
pdf
arx
 Braid groups and euclidean simplices (with E. Leyton Chisholm)
in Configuration Spaces:Geometry, Topology and Representation
theory, SpringerINDAM series (2016), 291311.
pdf
arx
 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), 82114. (survey article)
pdf
arx
 Artin groups of euclidean type (with
R. Sulway) Inventiones
Mathematicae (2017), 152 (online version).
pdf
arx
 The mysterious geometry of Artin groups, in Winter
Braids Lecture Notes, 4 (2017), 130.
pdf
wbln (survey article)
 Undesired parking spaces and contractible pieces of the
noncrossing partition link, (with Michael
Dougherty) Electronic
Journal of Combinatorics (2018),
113.
pdf
arx
 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)
 Computing reflection length in an affine Coxeter group
(with Joel Lewis,
Kyle Petersen and Petra Schwer), Transactions of the AMS,
371, (2019), 40974127.
pdf
arx
 Boundary braids, (with Michael Dougherty and Stefan
Witzel), Algebraic
& Geometric Topology 207 (2020), 35053560.
pdf
arx
 Critical points, critical values, and a determinant identity
for complex polynomials (with Michael
Dougherty), Proceedings of the AMS 148
(2020), 52775289.
pdf
 A complex euclidean reflection group with a nonpositively curved complement
complex, (with Ben Coté), Groups, Geometry and Dynamics 15 (2021), 9891013.
pdf
arx
 Tits alternative for groups acting properly on 2dimensional
recurrent complexes,
(with Damian Osajda and Piotr
Przytycki), Advances
in Mathematics 391 (2021).
pdf
arx (3 page appendix)
to appear
 Geometric combinatorics of polynomials I: the case of a single
polynomial (with Michael Dougherty), to appear in the Journal
of Algebra arx (30 pages)
 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)
 Factoring isometries of quadratic spaces into reflections,
(with Giovanni Paolini), to appear in the Journal
of Algebra arx (30 pages)
submitted
 Fixed points of parking functions, (with Hugh Thomas and
Nathan Williams), pdf
arx (37 pages)
 Dual braids and the braid arrangement (survey)
pdf (15 pages)
preprints
 Noncrossing hypertrees,
pdf
arx (53 pages)
software
other writings
 Geometric semigroup theory, (with J. Rhodes and B. Steinberg)
(66 pages) pdf
arx
 Curvature and computation (expository) (10 pages)
pdf
arx
 The infinite cyclohedron and its automorphism group, (with
A. Fossas Tenas) (18 pages)
pdf
arx
 The exceptional symmetry (short note) (8
pages)
pdf
arx
 An introduction to Garside structures (28 pages)
pdf
 The 0/1Borsuk conjecture is generically true for each fixed
diameter, (with G. Ziegler)
unpublished (8 pages)
pdf
slides
Here are some slides from a minicourse 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