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Aperiodicity, rotational tiling spaces and topological space groups (2021)
Journal Article
Hunton, J., & Walton, J. (2021). Aperiodicity, rotational tiling spaces and topological space groups. Advances in Mathematics, 388, Article 107855. https://doi.org/10.1016/j.aim.2021.107855

We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational structure... Read More about Aperiodicity, rotational tiling spaces and topological space groups.

Chaotic Delone Sets (2021)
Journal Article
Alvarez Lopez, J. A., Barral Lijo, R., Hunton, J., Nozawa, H., & Parker, J. R. (2021). Chaotic Delone Sets. Discrete and Continuous Dynamical Systems - Series A, 41(8), 3781-3796. https://doi.org/10.3934/dcds.2021016

We present a definition of chaotic Delone set and establish the genericity of chaos in the space of (ϵ,δ)-Delone sets for ϵ≥δ. We also present a hyperbolic analogue of the cut-and-project method that naturally produces examples of chaotic Delone sets... Read More about Chaotic Delone Sets.

The homology core of matchbox manifolds and invariant measures (2018)
Journal Article
Clark, A., & Hunton, J. (2019). The homology core of matchbox manifolds and invariant measures. Transactions of the American Mathematical Society, 371(3), 1771-1793. https://doi.org/10.1090/tran/7398

We consider the topology and dynamics associated with a wide class of matchbox manifolds, including spaces of aperiodic tilings and suspensions of higher rank (potentially nonabelian) group actions on zero-dimensional spaces. For such a space we intr... Read More about The homology core of matchbox manifolds and invariant measures.

Topological Invariants for Tilings (2017)
Conference Proceeding
Hunton, J. (2017). Topological Invariants for Tilings. In M. Baake, D. Damanik, J. Kellendonk, & D. Lenz (Eds.), . https://doi.org/10.4171/owr/2017/46

The mathematical theory of aperiodic order grew out of various predecessors in discrete geometry, harmonic analysis and mathematical physics, and developed rapidly after the discovery of real world quasicrystals in 1982 by Shechtman. Many mathematica... Read More about Topological Invariants for Tilings.

Spaces of Projection Method Patterns and their Cohomology (2015)
Book Chapter
Hunton, J. (2015). Spaces of Projection Method Patterns and their Cohomology. In J. Kellendonk, D. Lenz, & J. Savinien (Eds.), Mathematics of aperiodic order (105-135). Birkhäuser Verlag. https://doi.org/10.1007/978-3-0348-0903-0_4

We explain from the basics why the Čech cohomology of a tiling space can be realised in terms of group cohomology, and use this to explain how to compute the cohomology of a projection pattern.

Integral cohomology of rational projection method patterns (2013)
Journal Article
Hunton, J., Gähler, F., & Kellendonk, J. (2013). Integral cohomology of rational projection method patterns. Algebraic & geometric topology, 13(3), 1661-1708. https://doi.org/10.2140/agt.2013.13.1661

We study the cohomology and hence K–theory of the aperiodic tilings formed by the so called “cut and project” method, that is, patterns in d –dimensional Euclidean space which arise as sections of higher dimensional, periodic structures. They form on... Read More about Integral cohomology of rational projection method patterns.

The K-Theory of C*-Algebras with Finite Dimensional Irreducible Representations (2005)
Journal Article
Hunton, J., & Shchukin, M. (2006). The K-Theory of C*-Algebras with Finite Dimensional Irreducible Representations. Integral Equations and Operator Theory, 54(1), https://doi.org/10.1007/s00020-004-1346-0

We study the K-theory of unital C *-algebras A satisfying the condition that all irreducible representations are finite and of some bounded dimension. We construct computational tools, but show that K-theory is far from being able to distinguish betw... Read More about The K-Theory of C*-Algebras with Finite Dimensional Irreducible Representations.

Cohomology of canonical projection tilings (2002)
Journal Article
Forrest, A., Hunton, J., & Kellendonk, J. (2002). Cohomology of canonical projection tilings. Communications in Mathematical Physics, 226, 289-322

Chromatic characteristic classes in ordinary group cohomology (2002)
Journal Article
Green, D., Hunton, J., & Schuster, B. (2003). Chromatic characteristic classes in ordinary group cohomology. Topology (Oxford), 42(1), 243-263. https://doi.org/10.1016/s0040-9383%2802%2900011-3

We study a family of subrings, indexed by the natural numbers, of the mod p cohomology of a finite group G. These subrings are based on a family of vn-periodic complex oriented cohomology theories and are constructed as rings of generalised character... Read More about Chromatic characteristic classes in ordinary group cohomology.

Higher v_n torsion in Lie groups (1998)
Journal Article
Hunton, J., Mimura, M., Nishimoto, T., & Schuster, B. (1998). Higher v_n torsion in Lie groups. Journal of the Mathematical Society of Japan, 50(4), 801-818

Coalgebraic algebra (1998)
Journal Article
Hunton, J., & Turner, P. (1998). Coalgebraic algebra. Journal of Pure and Applied Algebra, 129, 297-313

A rational approach to Hopf rings (1995)
Journal Article
Hunton, J., & Ray, N. (1995). A rational approach to Hopf rings. Journal of Pure and Applied Algebra, 101, 313-333

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