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- W2018136119 abstract "This paper presents a new method for using cup product information to draw conclusions about the Lusternik–Schnirelmann category of a space. The key idea is that of the Hopf set in X of a map f : S n−1 →L ; if K = L ∪ f D n ⊆ X , then cat X ( K )=cat X ( L ) if and only if ∗ is in the Hopf set in X of f . The main result explicitly constructs elements of the Hopf set in X of f in terms of members of the Hopf set in X of the attaching maps of lower dimensional cells. Applications include: a calculation of the category of Sp (2) without higher order cohomology operations; new, easily used upper bounds for Lusternik–Schnirelmann category that apply to any space; and new information about the category of the CW skeleta of loop spaces and free loop spaces on even-dimensional spheres." @default.
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- W2018136119 date "2003-03-01" @default.
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- W2018136119 title "Decomposition of the diagonal map" @default.
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- W2018136119 doi "https://doi.org/10.1016/s0040-9383(01)00022-2" @default.
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