Noncommutative topological dynamics and compact actions on C∗-algebras
Journal of Functional Analysis, 1984 The classical notions of topological transitivity and minimality of a topological dynamical system are extended and analyzed in the context of \(C^*\)-dynamical systems. These notions are compared with other notions naturally arising in noncommutative ergodic theory. As an application, a \(C^*\)-algebra version of a theorem of \textit{H.
LONGO, ROBERTO, Peligrad, Costel
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A comparison of Hochschild homology in algebraic and smooth settings
Bulletin of the London Mathematical Society, Volume 57, Issue 4, Page 1249-1269, April 2025.Abstract Consider a complex affine variety V∼$\tilde{V}$ and a real analytic Zariski‐dense submanifold V$V$ of V∼$\tilde{V}$. We compare modules over the ring O(V∼)$\mathcal {O} (\tilde{V})$ of regular functions on V∼$\tilde{V}$ with modules over the ring C∞(V)$C^\infty (V)$ of smooth complex valued functions on V$V$.
David Kazhdan, Maarten Solleveld
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A noncommutative geometric analysis of a sphere–torus topology change [PDF]
Journal of Geometry and Physics, 2004 18 pages. 16 small eps figures.
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TOPOLOGICAL STATES OF MATTER AND NONCOMMUTATIVE GEOMETRY [PDF]
Bulletin of the Australian Mathematical Society, 2016 This thesis examines topological states of matter from the perspective of noncommutative geometry and KK-theory. Examples of such topological states of matter include the quantum Hall effect and topological insulators. For the quantum Hall effect, we consider a continuous model and show that the Hall conductance can be expressed in terms of the index ...
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A noncommutative version of Farber's topological complexity [PDF]
Topological Methods in Nonlinear Analysis, 2017 9 pages; minor mistakes removed; to appear in Topological Methods in Nonlinear ...
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A TOPOLOGICAL MIRROR SYMMETRY ON NONCOMMUTATIVE COMPLEX TWO-TORI
Journal of the Korean Mathematical Society, 2006 The purpose of this paper is to study an aspect of a topological mirror symmetry on elliptic curves starting from the paper of \textit{A. N. Tyurin} [Izv. Math. 64, No. 2, 363--437 (2000; Zbl 1039.53058)] which compares the moduli spaces of stable bundles and supercycles.
Kim, Eunsang, Kim, Hoil
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Noncommutative Topological Quantum Field Theory-Noncommutative Floer Homology
, 2005 We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology 3-spheres. There is also a physical motivation: one would like to construct a noncommutative topological quantum ...
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Random finite noncommutative geometries and topological recursion
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their InteractionsIn this paper, we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples {(\mathcal{A}, \mathcal{H}, D, \gamma, J)} , called random matrix ...
Shahab Azarfar, Masoud Khalkhali
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Minimal non-abelian nodal braiding in ideal metamaterials. [PDF]
Nat Commun, 2023 Qiu H +5 more
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A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions. [PDF]
Lett Math Phys, 2022 Pérez-Sánchez CI.
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