Results 1 to 10 of about 19,905 (78)
Codes on Graphs: Models for Elementary Algebraic Topology and Statistical Physics [PDF]
IEEE Transactions on Information Theory, 2017 This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic $(n, k)$ group
G. David Forney
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Tame topology of arithmetic quotients and algebraicity of Hodge loci [PDF]
Journal of The American Mathematical Society, 2018 In this paper we prove the following results: 1 ) 1) We show that any arithmetic quotient of a homogeneous space admits a natural real semi-algebraic structure for which its Hecke correspondences are semi-algebraic. A
B. Klingler
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The Topology of the Cosmic Web in Terms of Persistent Betti Numbers [PDF]
, 2016 We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its ...
Pratyush Pranav +6 more
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Invertible topological field theories [PDF]
Journal of Topology, 2017 A d$d$ ‐dimensional invertible topological field theory (TFT) is a functor from the symmetric monoidal (∞,n)$(\infty,n)$ ‐category of d$d$ ‐bordisms (embedded into R∞$\mathbb {R}^\infty$ and equipped with a tangential (X,ξ)$(X,\xi)$ ‐structure) that ...
Christopher J. Schommer-Pries
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Review article: Dynamical systems, algebraic topology and the climate sciences
Nonlinear Processes in Geophysics, 2023 . The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory.
M. Ghil, D. Sciamarella
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European Radiology Experimental, 2022 Background Primary sclerosing cholangitis (PSC) is a chronic cholestatic liver disease that can lead to cirrhosis and hepatic decompensation. However, predicting future outcomes in patients with PSC is challenging.
Yashbir Singh +20 more
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Non-Commutative Localization in Algebra and Topology: Invariants of boundary link cobordism II. The Blanchfield-Duval form [PDF]
, 2004 We use the Blanchfield-Duval form to define complete invariants for the cobordism group C_{2q-1}(F_\mu) of (2q-1)-dimensional \mu-component boundary links (for q\geq2). The author solved the same problem in math.AT/0110249 via Seifert forms.
Desmond Sheiham
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Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie [PDF]
, 2006 We use a version of the method of Deligne-Illusie to prove that the Hodge-to-de Rham, a.k.a. Hochschild-to-cyclic spectral sequence degenerates for a large class of associative, not necessariyl commutative DG algebras. This proves, under some assumption,
Dmitry Kaledin
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Michael Atiyah’s work in algebraic topology
Bulletin of the American Mathematical Society, 2021 In 1960 algebraic topology was at the centre of the mathematical stage, but Michael Atiyah burst into the field and changed its focus and its language.
G. Segal
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The Lambrechts-Stanley Model of Configuration Spaces [PDF]
, 2018 We prove the validity over $\mathbb{R}$ of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth manifolds, answering a conjecture of Lambrechts--Stanley. We get as a result that the real homotopy type
Idrissi, Najib
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