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- W3037321851 abstract "Abstract Let C be a model category with an initial object <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>⌀</m:mi> </m:math> ${varnothing }$ and functorial factorizations. Let <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>S</m:mi> <m:mo>:</m:mo> <m:mi>C</m:mi> <m:mo>→</m:mo> <m:mi>C</m:mi> </m:mrow> </m:math> ${S : C rightarrow C}$ be the suspension functor. An object X of C is said to be charged if it comes equipped with a map <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>S</m:mi> <m:mi>⌀</m:mi> <m:mo>→</m:mo> <m:mi>X</m:mi> </m:mrow> </m:math> ${S varnothing rightarrow X}$ . If Y is any object of C , then S Y has a preferred charge, given by applying suspension to the map <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>⌀</m:mi> <m:mo>→</m:mo> <m:mi>Y</m:mi> </m:mrow> </m:math> ${varnothing rightarrow Y}$ . This motivates the question of whether a given charged object is a suspension up to a weak equivalence in a way that preserves charge structures. We study this question in the context of spaces over a given space, where we give a complete obstruction in a certain metastable range. As an application we show how this can be used to study when an embedding into a smooth manifold of the form N × I compresses to an embedding into N ." @default.
- W3037321851 created "2020-07-02" @default.
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- W3037321851 date "2013-11-23" @default.
- W3037321851 modified "2023-10-14" @default.
- W3037321851 title "Charged spaces" @default.
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- W3037321851 doi "https://doi.org/10.1515/forum-2013-0096" @default.
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