Classifying spaces and spectral sequences
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The Mayer-Vietoris blowup and spectral sequence permit parallelization of homology computation into calculations of much smaller complexes.
“there is a construction known as the Mayer-Vietoris blowup , and a corresponding computational device known as the Mayer-Vietoris spectral sequence , which permits the parallelization of the homology computation into calculations of much smaller complexes.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Segal (1968, § 4)
The nerve theorem gives sufficient conditions for a much smaller construction based on a covering of the space to compute homology accurately.
“The socalled nerve theorem , which follows directly from the construction in Segal (1968, § 4), gives sufficient conditions for a much smaller construction based on a covering of the space to compute the homology accurately.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Segal (1968, § 4)
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- Authors
- Segal, G.
- Corresponding author
- Segal, Graeme
- ORCID
- Segal, Graeme
- Venue
- Publications Mathématiques de l'IHÉS
- Publisher
- MathDoc/Centre Mersenne
- Published
- 1968-01-07
- Volume
- 34
- Pages
- 105-112
- ISSN
- 0073-8301 (ISSN-L)
- 1618-1913
- OpenAlex
- W2043445128
- Cited by
- 764
- References
- 15
- Citations by year
- 2026: 7 · 2025: 15 · 2024: 8 · 2023: 7 · 2022: 12 · 2021: 25 · 2020: 47 · 2019: 19 · 2018: 31 · 2017: 23 · 2016: 24 · 2015: 16 · 2014: 24 · 2013: 18 · 2012: 25
- FWCI
- 2.02
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Publications mathématiques de l IHÉS (publishedVersion)
- French digital mathematics library (Numdam) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Keywords
- classifying spaces, spectral sequences
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