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Creators/Authors contains: "Isaksen, Daniel C"

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  1. ; ; ; ; (, Advances in Mathematics)
    Free, publicly-accessible full text available December 1, 2025
  2. ; ; (, Pacific Journal of Mathematics)
    We compute the $$v_1$$-periodic $$\mathbb{R}$$-motivic stable homotopy groups. The main tool is the effective slice spectral sequence. Along the way, we also analyze $$\mathbb{C}$$-motivic and $$\eta$$-periodic $$v_1$$-periodic homotopy from the same perspective. 
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  3. ; ; (, European Mathematical Society Press)
    Beliaev, Dmitry; Smirnov, Stanislav (Ed.)
    We consider the problem of computing the stable homotopy groups of spheres, including applications and history. We describe a new technique that yields streamlined computations through dimension 61 and gives new computations through dimension 90 with very few exceptions. We discuss questions and conjectures for further study, including a new approach to the computation of motivic stable homotopy groups over arbitrary base fields. We provide complete charts for the Adams spectral sequence through dimension 90. 
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    Accepted Manuscript Full Text Available
  4. ; ; ; (, Algebraic & Geometric Topology)
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  5. ; ; (, Publications mathématiques de l'IHÉS)
    Abstract Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic Adams spectral sequence for $$C\tau $$ C τ and the algebraic Novikov spectral sequence for $$BP_{*}$$ B P ∗ , we compute the classical and motivic stable homotopy groups of spheres from dimension 0 to 90, except for some carefully enumerated uncertainties. 
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  6. ; (, Journal of Topology)
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  7. ; ; ; (, Journal of the European Mathematical Society)
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  8. ; ; (, Proceedings of the American Mathematical Society)
    null (Ed.)
    Full Text Available 
  9. ; ; (, Proceedings of the National Academy of Sciences)
    We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is therefore less prone to error. The main mathematical tool is the Adams spectral sequence. 
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  10. ; (, Documenta mathematica)
    null (Ed.)
    We use the C2-equivariant Adams spectral sequence to compute part of the C2-equivariant stable homotopy groups π^{C2}_{n,n}. This allows us to recover results of Bredon and Landweber on the image of the geometric fixed-points map π^{C2}_{n,n}→π_0. We also recover results of Mahowald and Ravenel on the Mahowald root invariants of the elements 2^k. 
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