Research
PDFs of all
papers can be obtained directly from me
2023
84. Introduction to inverse semigroups, to appear as a
book chapter, 64pp, arXiv:2304.13580.
83. Noncommutative Stone duality, in Semigroups, algebras
and operator theory (A. A. Ambily, V. B. Kiran Kumar eds)
Springer, 11--66. Book chapter.
82. Higher dimensional generalizations of the Thompson
groups via higher rank graphs, with A. Sims and A. Vdovina,
Journal of Pure and Applied Algebra 228
(2004), 107456.
2022
81. Semigroup theory comes in from the cold, LMS
Newletter, Issue 499, March 2022. This is a survey article that
sets semigroup theory in a broader mathematical context.
2021
80. A generalization of higher rank graphs, with A. Vdovina,
Bull. Austral. Math. Soc, appeared online
26 July 2021.
79. Morita equivalence of pseudogroups, with P. Resende, Journal
of Algebra 586, 718--755.
78. The polycyclic inverse monoids and the Thompson groups
revisited, in (P. G. Romeo, A. R. Rajan eds) Semigroups,
categories and partial algebras ICSAA 2019, Springer,
Proc. in Maths and Stats, volume 345. Book chapter.
77. On Ehresmann semigroups, Semigroup Forum,
published online June.
76. The universal Boolean inverse semigroup presented by the
abstract Cuntz-Krieger relations, with Alina Vdovina, Journal
of Noncommutative Geometry 15, 279--304.
2020
75. Higher dimensional generalizations of the Thompson
groups, with Alina Vdovina, Advances in Mathematics 369,
107191.
74. The Booleanization of an inverse semigroup,
Semigroup
Forum 100 (2020), 283--314.
73.
Recent developments in inverse semigroup theory,
Semigroup
Forum 100 (2020), 103--118.
2019
72. A Tribute to John B. Fountain, with V. A. R.
Gould, Semigroup Forum 99 (2019), 1--8.
2017
71. Tarski monoids: Matui's spatial realization
theorem, Semigroup Forum. 95 (2017),
379--404.
70. Levi categories and graphs of groups, with A.
Wallis, TAC 32 (2017), 780--802.
69. A
perspective on non-commutative frame theory, with G.
Kudryavtseva, Adv. Math. 311 (2017),
378--468.
68. AF inverse
monoids and the structure of countable MV-algebras, with P.
Scott, J. P. A. A. 221 (2017),
45--74.
2016
67. Subgroups of the
group of homeomorphisms of the Cantor space and a duality
between a class of inverse monoids and a class of Hausdorff
etale groupoids, J. Alg. 462 (2016),
77--114.
66. Invariant means on Boolean inverse monoids,
with G. Kudryavtseva, D. H. Lenz, P. Resende, Semigroup
Forum 92 (2016), 77--101.
2015
65. Boolean sets, skew Boolean algebras, and a non-commutative
Stone duality, with G. Kudryavtseva, Alg. Univ.
75 (2015), 1--19.
64. A correspondence between a class of monoids and
self-similar group actions II, with A. Wallis, IJAC 25
(2015), 633--668.
63. The classifying space of an inverse semigroup, with G.
Kudryavtseva, Periodica Math. Hung. 70 (2015),
122--129.
2014
62. David Rees 1918--2013, with L. O'Carroll, S. Rees, Semigroup
Forum 88 (2014), 513--522.
61. Graph inverse semigroups: their characterization and
completion, with D. Jones, Journal of Algebra 409
(2014), 444--473.
60. The structure of generalized inverse semigroups, with
G. Kudryavtseva, Semigroup Forum 89 (2014),
199--216.
2013
59. The etale groupoid of an inverse semigroup as a groupoid
of filters, with S. W. Margolis and B. Steinberg,
J. Aust. Math. Soc. 94,
234--256.
58. Pseudogroups and their etale groupoids, with D. Lenz, Advances
in Maths 244 (2013), 117--170.
57. Morita equivalence of inverse semigroups, with B. Afara, Periodica
Math Hung. 66 (2013), 119--130.
2012
56. Non-commutative Stone duality: inverse semigroups,
topological groupoids and C*-algebras, IJAC 22, 1250058
(2012), 47pp.
55. Morita equivalence of semigroups with locally
commuting idempotents, with B. Afara, Communications
in Algebra 40,
1982--1996.
54. Strong
representation of the polycyclic inverse monoids: cycles and
atoms, with D. Jones, Periodica
Math.
Hung.
64, 53-87.
2011
53. Characterizations of Morita equivalent inverse
semigroups, with J. Funk and B. Steinberg, J. Pure Appl. Algebra 215, 2262-2279.
52. Morita theory for semigroups with local
units, J. Pure Appl.
Algebra 215, 455--470.
51. Generalized heaps, inverse semigroups and Morita
equivalence, Algebra
Universalis 66
(2011), 317--330.
2010
50. Compactable semilattices, Semigroup Forum 81, 187--199.
49. A
non-commutative generalization of Stone duality, J.
Austral. Math. Soc.
88, 385--404.
This paper won
the Mahony-Neumann-Room Prize of the Australian
Mathematical Society 2017.
2009
48. Primitive partial permutation representations of the
polycyclic monoids and branching function systems, Periodica Math. Hung. 52, 189--207.
2008
47. Semigroups related to subshifts of graphs, Mathematics Studies of the
Estonian Mathematical Society 3, (edited by V. Laan,
S. Bulman-Fleming, R. Kaschek),
92--107.
46. A correspondence between a class of monoids and
self-similar group actions I, Semigroup
Forum 76,
489-517.
2007
45. The polycyclic monoids P_{n} and the Thompson groups
V_{n,1}, Communications in
algebra 35,
4068--4087.
44. A class of subgroups of Thompson's group V, Semigroup Forum 75, 241--252.
43. In McAlister's footsteps: a random ramble around the
P-theorem, with S. Margolis Proceedings of the International Conference on
Semigroups and Languages, Lisbon 2005,
(eds Andre, Fernandes, Branco, Gomes, Fountain and Meakin) World
Scientific, 2007, 145--163.
42. Orthogonal completions of
the polycyclic monoids, Communications
in Algebra 35,
1651--1660.
2006
41. A correspondence between balanced varieties and inverse
monoids, Inter. J. Alg. and
Computation 16, 887--924.
40. Expansions of inverse semigroups, with S.
Margolis and B. Steinberg Journal of the Australian
Mathematical Society 80,
205--228.
2005
39. Constructing ordered
groupoids, Cahiers de topologie
et geometrie differentielle categoriques 46, 123--138.
2004
38. Partial actions of
groups, with J. Kellendonk, International Journal
of Algebra and Computation 14,
87--114.
37. Ordered groupoids and
etendues, with B. Steinberg Cahiers de topologie et
geometrie differentielle categoriques XLV, 82--108.
36. Ordered groupoids and
left cancellative categories, Semigroup
Forum 68,
458--476.
35. One dimensional tiling semigroups, Semigroup
Forum 68, 159--176.
34. Universal groups for
point-sets and tilings, with J. Kellendonk Journal of Algebra 276, 462--492.
2002
33. E*-unitary inverse semigroups, in
Semigroups,
algorithms, automata and languages (eds G M S Gomes, J-E Pin, P V Silva) World
Scientific, 195--214.
32. The homotopy theory of
inverse semigroups, with J. Matthews and T. Porter International
Journal of Algebra and Computation 12, 755--790.
2001
31. Rees matrix covers for a
class of semigroups with locally commuting idempotents, with
T. Khan Proc. Edinburgh Math. Soc. 44, 173--186.
30. Variants of regular
semigroups, with T. Khan Semigroup Forum 62,
358--374.
2000
29. A characterisation of a
class of semigroups with locally commuting idempotents, with T.
Khan Periodica Mathematica Hungarica 40,
85--107.
28. Tiling semigroups, with
J. Kellendonk Journal of Algebra 224,
140--150.
27. Enlargements and coverings
by Rees matrix semigroups, with L. Marki Monatshefte
fuer Mathematik 129, 191--195.
26. Rees matrix semigroups over
semigroupoids and the structure of a class of abundant semigroups,
Acta Scientiarum Mathematicarum 66, 517--540.
1999
25. An application of groupoids
of fractions to inverse semigroups, with H. James Periodica
Mathematica Hungarica 38 , 43--54.
24. The structure of 0-E-unitary
inverse semigroups I: the monoid case, Proc. Edinburgh
Math. Soc. 42, 497--520.
23. Constructing inverse
semigroups from category actions, J. of Pure and Applied
Algebra 137, 57--101.
1998
22. McAlister semigroups,
Journal of Algebra 202, 276--294.
21. The Moebius inverse monoid,
Journal of Algebra 200, 428--438.
20. An application of polycyclic
monoids to rings, with P. Hines Semigroup Forum
56, 146--149.
1997
19. Unit regular monoids,
with J. B. Hickey Proc. Royal Soc. Edinburgh: Section A
Mathematics, 127 , 127--143.
1996
18. Enlargements of regular
semigroups, Proc. Edinburgh Math. Soc. 39,
425--460.
17. A class of actions of
inverse semigroups, Journal of Algebra 179,
570--598.
1994
16. Almost factorisable inverse
semigroups, Glasgow Mathematical J. 36, 97--111.
15. Extending partial
isomorphisms and McAlister's covering theorem ,
Semigroup Forum 48 , 18--27.
1993
14. A note on a paper of
Joubert, Semigroup Forum 47, 389--392.
13. Coverings and embeddings of
inverse semigroups, Proc. Edinburgh Math. Soc. 36,
399--419.
12. Congruences on ordered
groupoids, Semigroup Forum 47, 150--167.
11. An equivalence theorem for
inverse semigroups, Semigroup Forum 47, 7--14.
1992
10. The geometric theory of
inverse semigroups II: E-unitary covers of inverse
semigroups, J.
Pure and Applied Algebra 83, 121--139.
1991
9. Semigroups and ordered
categories I: the reduced case, Journal of Algebra 141,
422--462.
1990
8. The geometric theory of
inverse semigroups I: $E$-unitary inverse semigroups, J.
Pure and Applied Algebra 67, 151--177.
7. Rees matrix semigroups,
Proc. Edinburgh Math. Soc. 33, 23--37.
1989
6. An order theoretic
characterisation of locally orthodox semigroups,
Semigroup Forum 39, 113--116.
1987
5. Rees matrix covers for a
class of abundant semigroups, Proc. Royal Soc. Edinburgh:
Section A Mathematics, 107, 109--120.
4. Abundant Rees
matrix semigroups,
J. Australian Math. Soc. (Series~A) 42,
132--142.
3. The natural partial order on
an abundant semigroup, Proc. Edinburgh Math. Soc. 30,
169--186.
1986
2. The structure of type A
semigroups, Quart. J. Maths. 37, 279--298.
1985
1. The translational hull of an
adequate semigroup, with J. B. Fountain Semigroup Forum 32,
79--86.