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Spaces of functions and sections with paracompact domain

Part of: Spectral sequences Homotopy theory

Published online by Cambridge University Press:  21 November 2023

Jaka Smrekar Open the ORCID record for Jaka Smrekar [Opens in a new window]
Jaka Smrekar*
Affiliation:
Fakulteta za matematiko in fiziko, Jadranska ulica 19, SI-1111 Ljubljana, Slovenia ([email protected])
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Abstract

We study spaces of continuous functions and sections with domain a paracompact Hausdorff k-space $X$ and range a nilpotent CW complex $Y$, with emphasis on localization at a set of primes. For $\mathop {\rm map}\nolimits _\phi (X,\,Y)$, the space of maps with prescribed restriction $\phi$ on a suitable subspace $A\subset X$, we construct a natural spectral sequence of groups that converges to $\pi _*(\mathop {\rm map}\nolimits _\phi (X,\,Y))$ and allows for detection of localization on the level of $E^2$. Our applications extend and unify the previously known results.

Keywords

Function spaceFederer spectral sequencelocalization

MSC classification

Primary: 55T99: None of the above, but in this section 55P60: Localization and completion 55P15: Classification of homotopy type
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 23
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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