"boundary homomorphism" meaning in English

See boundary homomorphism in All languages combined, or Wiktionary

Noun

Forms: kth boundary homomorphism [canonical], boundary homomorphisms [plural]
Head templates: {{en-noun|head=kth boundary homomorphism}} kth boundary homomorphism (plural boundary homomorphisms)
  1. (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. Categories (topical): Algebraic topology
    Sense id: en-boundary_homomorphism-en-noun-TAE-Ploz Topics: algebraic-topology, mathematics, sciences, topology
  2. (algebraic topology, in greater generality) A homomorphism that operates on the kth element in a chain complex. Categories (topical): Algebraic topology
    Sense id: en-boundary_homomorphism-en-noun-Ugg7Jf5u Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 28 72 Disambiguation of Pages with 1 entry: 27 73 Disambiguation of Pages with entries: 24 76 Topics: algebraic-topology, mathematics, sciences, topology

Inflected forms

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  "forms": [
    {
      "form": "kth boundary homomorphism",
      "tags": [
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    },
    {
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebraic topology",
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            "Topology",
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            "Formal sciences",
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            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "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."
      ],
      "id": "en-boundary_homomorphism-en-noun-TAE-Ploz",
      "links": [
        [
          "algebraic topology",
          "algebraic topology"
        ],
        [
          "simplicial",
          "simplicial"
        ],
        [
          "chain complex",
          "chain complex"
        ],
        [
          "simplicial k-chains",
          "chain"
        ],
        [
          "oriented",
          "oriented"
        ],
        [
          "simplex",
          "simplex"
        ],
        [
          "formal sum",
          "formal sum"
        ],
        [
          "face",
          "face"
        ]
      ],
      "raw_glosses": [
        "(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"
      ],
      "topics": [
        "algebraic-topology",
        "mathematics",
        "sciences",
        "topology"
      ]
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          "parents": [
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            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "27 73",
          "kind": "other",
          "name": "Pages with 1 entry",
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          "_dis": "24 76",
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          "parents": [],
          "source": "w+disamb"
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      ],
      "glosses": [
        "A homomorphism that operates on the kth element in a chain complex."
      ],
      "id": "en-boundary_homomorphism-en-noun-Ugg7Jf5u",
      "links": [
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          "algebraic topology",
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      "raw_glosses": [
        "(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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    "Pages with 1 entry",
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  ],
  "forms": [
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      "form": "kth boundary homomorphism",
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "en:Algebraic topology"
      ],
      "glosses": [
        "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."
      ],
      "links": [
        [
          "algebraic topology",
          "algebraic topology"
        ],
        [
          "simplicial",
          "simplicial"
        ],
        [
          "chain complex",
          "chain complex"
        ],
        [
          "simplicial k-chains",
          "chain"
        ],
        [
          "oriented",
          "oriented"
        ],
        [
          "simplex",
          "simplex"
        ],
        [
          "formal sum",
          "formal sum"
        ],
        [
          "face",
          "face"
        ]
      ],
      "raw_glosses": [
        "(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"
      ],
      "topics": [
        "algebraic-topology",
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        "sciences",
        "topology"
      ]
    },
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        "en:Algebraic topology"
      ],
      "glosses": [
        "A homomorphism that operates on the kth element in a chain complex."
      ],
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          "algebraic topology",
          "algebraic topology"
        ],
        [
          "homomorphism",
          "homomorphism"
        ],
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          "chain complex"
        ]
      ],
      "raw_glosses": [
        "(algebraic topology, in greater generality) A homomorphism that operates on the kth element in a chain complex."
      ],
      "raw_tags": [
        "in greater generality"
      ],
      "topics": [
        "algebraic-topology",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "boundary homomorphism"
}

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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 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.

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