Research Papers and Preprints

Dynamical systems, aperiodic order and K-theory 

 

The cohomology and K-theory of commuting homeomorphisms of the Cantor set, (with Alan Forrest) Ergodic Theory and Dynamical Systems 19 (1999), 611-625.

Cohomology groups for projection point patterns, (with Alan Forrest and Johannes Kellendonk)

Proceedings, XIIIth International Congress of Mathematical Physics, (London, 2000), 333--339, Int. Press, Boston, MA, 2001. math-ph/0010050.

Cohomology of canonical projection tilings, (with Alan Forrest and Johannes Kellendonk) Communications in Mathematical Physics, 226 (2002), 289-322.

Topological invariants for projection point patterns, (with Alan Forrest and Johannes Kellendonk)

Memoirs of the American Mathematical Society, volume 159. American Mathematical Society, 2002 (120 pp). ISBN 0-8218-2965-3. math.AT/0010265.


The K-theory of C*-algebras with finite dimensional irreducible representations (with Mikhail Shchukin) Integral equations and operator theory 54 (2006), 89-96.

Torsion in tiling homology and cohomology, (with Franz Gaehler and Johannes Kellendonk). math-ph/0505048. 

Integer Cech Cohomology of Projection Tilings, (with Franz Gaehler and Johannes Kellendonk), Proceedings, Xth International Congress of Quasicrystals, Zeitschrift fuer Kristallographie 223 (2008), 801-804.
 
Cohomology of substitution tiling spaces, (with Marcy Barge, Beverly Diamond and Lorenzo Sadun), Ergodic Theory and Dynamical Systems 30 (2010), 1607-1627.
 
Tiling spaces, codimension one attractors and shape, (with Alex Clark), New York Journal of Mathematics; 18 (2012), 765-796. math.ds/1105.0835.

Coverings, the graded centre and Hochschild cohomology (with Ed Green and Nicole Snashall) Journal of Pure and Applied Algebra 212 (2008), 2691-2706. 
 
Integral cohomology of rational projection method patterns, (with Franz Gaehler and Johannes Kellendonk); to appear in Algebraic and Geometric Topology, math.KT/1202.2240v2.

Omega spectra, coalgebraic algebra and applications 

The structure of spaces representing a Landweber exact cohomology theory, (with Mike Hopkins)
Topology 34 (1995), 29-36.

A rational approach to Hopf rings, (with Nige Ray)
Journal of Pure and Applied Algebra 101 (1995), 313-333.

Coalgebraic algebra, (with Paul Turner)
Journal of Pure and Applied Algebra 129 (1998), 297-313.

The homology of spaces representing exact pairs of homotopy functors, (with Paul Turner)
Topology 38 (1999), 621-634.

Complete cohomology theories and the homology of their omega spectra,
Topology 41 (2002), 931-943.

Chromatic characteristic classes in ordinary group cohomology, (with David Green and Bjoern Schuster)
Topology, 42 (2003), 243-263. math.AT/0109019.

Subalgebras of group cohomology defined by infinite loop spaces, (with Bjoern Schuster)
Topology 44 (2005), 689-704. hs.ps

On the coalgebraic ring and Bousfield-Kan spectral sequence for a Landweber exact spectrum, (with Martin Bendersky)
Proceedings of the Edinburgh Mathematical Society 47 (2004), 513-532.


Other homotopy theory

The Morava K-theories of wreath products,
Mathematical Proceedings of the Cambridge Philosophical Society 107 (1990), 309-318.

Detruncating Morava K-Theory,
London Mathematical Society Lecture Note Series 176, (1992), 35-43.

Continuous Morava K-Theory and the geometry of the In-adic tower, (with Andrew Baker)
Mathematica Scandinavica 75 (1994), 67-81.

The Boardman homomorphism,
The Cech centennial conference, American Mathematical Society,
Contemporary Mathematics 181 (1995), 251-262.

The complex oriented cohomology of extended powers,
Annales de l'Institute Fourier 48 (1998), 517-534.

Higher vn torsion in Lie groups, (with Mamoru Mimura, Tetsu Nishimoto and Bjoern Schuster)
Journal of the Mathematical Society of Japan 50 (1998), 801-818.

Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems, (with Frances Clarke and Nige Ray)
Annales de l'Institute Fourier 51 (2001), 297-336.

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