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); Algebraic and Geometric Topology 13 (2013), 1661-1708. 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.