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Adams operations on the twisted K-theory of compact Lie groups
In this paper, extending the results in Fok (Proc Am Math Soc 145:2799–2813, 2017), we compute Adams operations on the twisted K -theory of connected,...
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The local cohomology spectral sequence for topological modular forms
We discuss proofs of local cohomology theorems for topological modular forms, based on Mahowald–Rezk duality and on Gorenstein duality, and then make...
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The Convergences of Part of Algebraic Representatives
Both Adams spectral sequence and Adams–Novikov spectral sequence converge to the stable homotopy groups of sphere π * ( S ). Suppose an element x in the E
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Stable homotopy groups of spheres: from dimension 0 to 90
Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic...
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Adams Operations in Commutative Algebra
The classical Adams operations are defined on the Grothendieck group of algebraic vector bundles on a scheme, and are related to Grothendieck’s...
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Computations of the Adams-Novikov E2-term
The author introduces the notion of a minimal resolution for BP * BP -comodules, and gives an effective algorithm to produce minimal resolutions. This...
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Spectral decimation for a graph-directed fractal pair
We introduce a graph-directed pair of planar self-similar sets that possess fully symmetric Laplacians. For these two fractals, due to Shima’s...
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Synthetic spectra and the cellular motivic category
To an Adams-type homology theory we associate the notion of a synthetic spectrum; this is a product-preserving sheaf on the site of finite spectra...
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Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations
The higher Leray–Serre spectral sequence associated with a tower of fibrations represents a generalization of the classical Leray–Serre spectral...
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Topological Hecke eigenforms
We study the eigenforms of the action of A. Baker’s Hecke operators on the holomorphic elliptic homology of various topological spaces. We prove a...
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Four Families of Nontrivial Product Elements in the Stable Homotopy Groups of Spheres
In this paper, the authors introduce a new effective method to compute the generators of the E 1 -term of the May spectral sequence. This helps them to...
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Linear multi-step methods and their numerical stability for solving gradient flow equations
In this paper, linear multi-step methods are used to numerically solve gradient flow models, and the relations between different numerical...
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An H1 convergence of the spectral method for the time-fractional non-linear diffusion equations
The generalized discrete Gronwall inequality is applied to analyze the optimal H 1 error estimate of the time-step** spectral method for the...