Cech and Steenrod homotopy and the Quigley exact couple in strong shape and proper homotopy theory

DOI10.1016/0022-4049(82)90049-4zbMath0485.55009OpenAlexW1994164508MaRDI QIDQ1164292

Timothy Porter

Publication date: 1982

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(82)90049-4

zbMATH Keywords

shape groupsCech and Steenrod homotopyhomotopy groups for metric compactaHurewicz isomorphism theoryQuigley exact couple in strong shape and proper homotopy theory

Mathematics Subject Classification ID

Shape theory (55P55) Steenrod-Sitnikov homologies (55N07) General theory of spectral sequences in algebraic topology (55T05) Shape groups (55Q07)

Related Items (14)

Self-overlays and symmetries of Julia sets of expanding maps ⋮ A theoretical framework for proper homotopy theory ⋮ The shape of the Julia set of an expanding rational map ⋮ Calculations of cylindricalp-homotopy groups ⋮ Proper pointed maps from ℝⁿ⁺¹to a σ-compact space ⋮ An embedding theorem for proper \(n\)-types ⋮ A closed simplicial model category for proper homotopy and shape theories ⋮ Sequential homology ⋮ Exact sequences and closed model categories ⋮ Unnamed Item ⋮ Fundamental groups and finite sheeted coverings ⋮ Reduced powers, ultrapowers and exactness of limits ⋮ Postnikov factorizations at infinity ⋮ On the relation between the fundamental groupoids of the classifying space and the nerve of an open cover

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homotopical approach to strong shape or completion theory
• Homotopy groups of pro-spaces
• Cech and Steenrod homotopy theories with applications to geometric topology
• Homotopy limits, completions and localizations
• Hurewicz Isomorphism Theorem for Steenrod Homology
• The Classification of Two-Dimensional Manifolds
• Conractible 3-Manifolds of Finite Genus at Infinity
• On Proper Homotopy Theory for Noncompact 3-Manifolds
• An exact sequence from the nth to the (n-1)-st fundamental group
• ČEch Homotopy I

This page was built for publication: Cech and Steenrod homotopy and the Quigley exact couple in strong shape and proper homotopy theory