See homology group in All languages combined, or Wiktionary
Download JSON data for homology group meaning in English (1.5kB)
{
"forms": [
{
"form": "kth homology group",
"tags": [
"canonical"
]
},
{
"form": "homology groups",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"head": "kth homology group"
},
"expansion": "kth homology group (plural homology groups)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
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"Entry maintenance"
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},
{
"kind": "topical",
"langcode": "en",
"name": "Algebraic topology",
"orig": "en:Algebraic topology",
"parents": [
"Algebra",
"Topology",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"glosses": [
"The quotient group of the kth cycle group modulo the kth boundary group (derived from the chain complex of, e.g., a given simplicial complex)."
],
"id": "en-homology_group-en-noun-2oO66kMj",
"links": [
[
"algebraic topology",
"algebraic topology"
],
[
"quotient group",
"quotient group"
],
[
"cycle group",
"cycle group"
],
[
"modulo",
"modulo"
],
[
"boundary group",
"boundary group"
],
[
"chain complex",
"chain complex"
],
[
"simplicial complex",
"simplicial complex"
]
],
"raw_glosses": [
"(algebraic topology) The quotient group of the kth cycle group modulo the kth boundary group (derived from the chain complex of, e.g., a given simplicial complex)."
],
"related": [
{
"word": "Betti number"
}
],
"topics": [
"algebraic-topology",
"mathematics",
"sciences",
"topology"
]
}
],
"word": "homology group"
}
{
"forms": [
{
"form": "kth homology group",
"tags": [
"canonical"
]
},
{
"form": "homology groups",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"head": "kth homology group"
},
"expansion": "kth homology group (plural homology groups)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "Betti number"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"en:Algebraic topology"
],
"glosses": [
"The quotient group of the kth cycle group modulo the kth boundary group (derived from the chain complex of, e.g., a given simplicial complex)."
],
"links": [
[
"algebraic topology",
"algebraic topology"
],
[
"quotient group",
"quotient group"
],
[
"cycle group",
"cycle group"
],
[
"modulo",
"modulo"
],
[
"boundary group",
"boundary group"
],
[
"chain complex",
"chain complex"
],
[
"simplicial complex",
"simplicial complex"
]
],
"raw_glosses": [
"(algebraic topology) The quotient group of the kth cycle group modulo the kth boundary group (derived from the chain complex of, e.g., a given simplicial complex)."
],
"topics": [
"algebraic-topology",
"mathematics",
"sciences",
"topology"
]
}
],
"word": "homology group"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c and c9440ce). 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.