"Poincaré space" meaning in All languages combined

{
  "forms": [
    {
      "form": "Poincaré spaces",
      "tags": [
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      "expansion": "Poincaré space (plural Poincaré spaces)",
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  "lang_code": "en",
  "pos": "noun",
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      "examples": [
        {
          "text": "Any closed, orientable, connected manifold is a Poincaré space.",
          "type": "example"
        }
      ],
      "glosses": [
        "An n-dimensional topological space with a distinguished element µ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th cohomology group."
      ],
      "id": "en-Poincaré_space-en-noun-dNQTmoVj",
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          "dimensional",
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        [
          "topological space",
          "topological space"
        ],
        [
          "homology",
          "homology"
        ],
        [
          "group",
          "group"
        ],
        [
          "cap product",
          "cap product"
        ],
        [
          "element",
          "element"
        ],
        [
          "cohomology",
          "cohomology"
        ],
        [
          "isomorphism",
          "isomorphism"
        ]
      ],
      "raw_glosses": [
        "(topology) An n-dimensional topological space with a distinguished element µ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th cohomology group."
      ],
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        "mathematics",
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      ],
      "wikipedia": [
        "Poincaré space"
      ]
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  "word": "Poincaré space"
}

{
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      "form": "Poincaré spaces",
      "tags": [
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  "lang_code": "en",
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      "examples": [
        {
          "text": "Any closed, orientable, connected manifold is a Poincaré space.",
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      ],
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        "An n-dimensional topological space with a distinguished element µ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th cohomology group."
      ],
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        [
          "topology",
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        ],
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          "homology",
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        [
          "group",
          "group"
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        [
          "cap product",
          "cap product"
        ],
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          "element",
          "element"
        ],
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          "cohomology",
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          "isomorphism",
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        "(topology) An n-dimensional topological space with a distinguished element µ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th cohomology group."
      ],
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      "wikipedia": [
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  "word": "Poincaré space"
}