See boundary homomorphism in All languages combined, or Wiktionary
Download JSON data for boundary homomorphism meaning in English (2.3kB)
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{
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"pos": "noun",
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"A group homomorphism on the group of simplicial k-chains induced by mapping each oriented k-simplex to a particular formal sum of its faces."
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"(algebraic topology, in a simplicial chain complex) A group homomorphism on the group of simplicial k-chains induced by mapping each oriented k-simplex to a particular formal sum of its faces."
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"glosses": [
"A homomorphism that operates on the kth element in a chain complex."
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"id": "en-boundary_homomorphism-en-noun-Ugg7Jf5u",
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"(algebraic topology, in greater generality) A homomorphism that operates on the kth element in a chain complex."
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"in greater generality"
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{
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"form": "kth boundary homomorphism",
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"A group homomorphism on the group of simplicial k-chains induced by mapping each oriented k-simplex to a particular formal sum of its faces."
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"(algebraic topology, in a simplicial chain complex) A group homomorphism on the group of simplicial k-chains induced by mapping each oriented k-simplex to a particular formal sum of its faces."
],
"raw_tags": [
"in a simplicial chain complex"
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"(algebraic topology, in greater generality) A homomorphism that operates on the kth element in a chain complex."
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.