Publications
K. C. H. Mackenzie
2005 Book:
Papers on multiple duality
 (with Alfonso GraciaSaz) Duality functors for $n$fold vector bundles,
arXiv:1209.0027
 (with Alfonso GraciaSaz) Duality functors for triple vector bundles,
Letters in Mathematical Physics, 90, 175200, 2009. DOI: 10.1007/s110050090346z
arXiv:0901.0203
 Duality and triple structures
pages 455 to 481 of The Breadth of Symplectic and Poisson
Geometry, Festschrift in Honor of Alan Weinstein, Birkhauser
2005, edited by J. E. Marsden and T. S. Ratiu.
math.DG/0406267
Paper on triple structures
Papers on doubles
 (with A. GraciaSaz, M. Jotz Lean and R. A. Mehta)
Double Lie algebroids and representations up to homotopy,
Journal of Homotopy and Related Structures, 13(2), 287319, (2018)
10.1007/s4006201701831
The main sequence of papers on doubles, in reverse logical order, is:
 Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids,
Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2011, Issue 658, Pages 193–245, DOI: 10.1515/CRELLE.2011.092.
Notation, with page numbers
 On symplectic double groupoids and the duality of
Poisson groupoids
Internat. J. Math. 10 (1999), 435456.
math.DG/9808005
 Double Lie algebroids and secondorder geometry, II
Adv. Math.
154 (2000), 4675.
dgga/9712013
 Double Lie algebroids and secondorder geometry, I.
Adv. Math., 94(2):180239, 1992.
pdf file

(with R. Brown.)
Determination of a double Lie groupoid by its core diagram.
J. Pure Appl. Algebra, 80(3):237272, 1992.
pdf file
An overview with background is in:
An introduction, written for people approaching from the
Poisson/symplectic point of view, is in:
 On certain canonical diffeomorphisms in symplectic and Poisson
geometry
Quantization, Poisson brackets and beyond, ed. Th. Voronov,
Contemporary Mathematics, 315, 2002, 187  198.
math.DG/0210384
Other papers on aspects of doubles:
 Affinoid structures and connections
Poisson Geometry, Banach Center Publications Volume 51 (2000), 175186. pdf file
 (with T. Mokri) Locally vacant double Lie groupoids and
the integration of matched pairs of Lie algebroids
Geom. Dedicata 77 (1999), 317330.
Papers on Poisson geometry
 (with A. Odzijewicz and A. Slizewska) Poisson geometry related to Atiyah sequences
SIGMA, 14, (2018)
10.3842/SIGMA.2018.005
 A unified approach to Poisson reduction
Lett. Math. Phys. 53(3) (2000), 215232. pdf file (not on arXiv)
 (with P. J. Higgins) Duality for basechanging morphisms of vector bundles, modules, Lie algebroids and
Poisson structures.
Math. Proc. Cambridge Philos. Soc. 114:471488. 1993.
If you want a good laugh, you could read the MR review of this paper.
If you do read it, note that none of the passages in quotation marks in the review actually occur in the paper.
Papers on Lie bialgebroids
 (with Ping Xu) Integration of Lie bialgebroids
Topology 39 (2000), 445467.
dgga/9712012
 (with Ping Xu.) Classical lifting processes and
multiplicative vector fields.
Quarterly J. Math.
Oxford (2), 49 (1998), 5985.
dgga/9710030
 (with Ping Xu.) Lie bialgebroids and Poisson groupoids.
Duke Math. J., 73(2):415452, 1994.
pdf
Papers on Lie algebroids and Lie groupoids in general
 (with Y. KosmannSchwarzbach) Differential operators and actions
of Lie algebroids
Quantization, Poisson brackets and beyond, ed. T. Voronov,
Contemporary Mathematics, 315, 2002, 213  233.
math.DG/0209337
 Lie algebroids and Lie pseudoalgebras.
Bull. London Math. Soc., 27(2):97147, 1995.
 (with P. J. Higgins) Algebraic constructions in the category
of Lie algebroids
J. Algebra, 129:194230, 1990.
 (with P. J. Higgins) Fibrations and quotients of differentiable
groupoids
J. London Math. Soc.(2) 42:101110, 1990.
 A note on Lie algebroids which arise from groupoid actions.
Cahiers Topologie Geom. Differentielle Categ. 28:283302. 1987.
Papers on principal bundles and connection theory
 Classification of principal bundles and Lie groupoids with prescribed
gauge group bundle.
J. Pure Appl. Algebra 58:181208, 1989. pdf of scan
 On extensions of principal bundles.
Ann. Global Anal. Geom. 6:141163, 1988.
 Integrability obstructions for extensions of Lie algebroids.
Cahiers Topologie Geom. Differentielle Categ.
28:2952, 1987. pdf of scan
Paper on cohomology of groupoids
 (as K. A. Mackenzie) Rigid cohomology of topological groupoids
J. Austral. Math. Soc. Ser. A. 26:277301, 1978. pdf of scan
`Rigid cohomology' is what became known shortly afterwards as continuous cohomology. The name `rigid' was chosen to
reflect the fact that the topology of the extensions which the theory classifies is (fibrewise) the direct product
of the topologies of the quotient and kernel.
1987 Book:
 Lie Groupoids and Lie Algebroids in Differential Geometry,
Cambridge University Press, 1987, xvi + 327 pages.
With the exception of the material on topological groupoids, most of this book has been incorporated in revised form
into my 2005 book.
The 1987 book is still of interest for reasons of priority : none of the original material had been published (or
offered for publication) elsewhere.
May 23, 2018
Homepage for K. C. H. Mackenzie