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The evaluation subgroup G *(U, X; f), which is a generalization of the Gottlieb group of X, is investigated. The key device for the study is an explicit Sullivan model for the connected component containing f of the function space of maps from U to X, which is derived from the general theory of such a model due to Brown and Szczarba (Trans Am Math Soc 349, 4931-4951, 1997). In particular, we show that non Gottlieb elements are detected by analyzing a Sullivan model for the map f and by looking at non-triviality of higher order Whitehead products in the homotopy group of X. The Gottlieb triviality of a fibration in the sense of Lupton and Smith (The evaluation subgroup of a fibre inclusion, 2006) is also discussed from the function space model point of view. Moreover, we proceed to consideration of the evaluation subgroup of the fundamental group of a nilpotent space. In consequence, the first Gottlieb group of the total space of each S-1-bundle over the n-dimensional torus is determined explicitly in the non-rational case."}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Hirato,  Y"}], "nameIdentifiers": [{"nameIdentifier": "36706", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "Kuribayashi,  K"}], "nameIdentifiers": [{"nameIdentifier": "36707", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "Oda,  N"}], "nameIdentifiers": [{"nameIdentifier": "36708", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2015-09-28"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "R-gottlieb-v12.pdf", "filesize": [{"value": "314.5 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_note", "mimetype": "application/pdf", "size": 314500.0, "url": {"label": "R-gottlieb-v12.pdf", "url": "https://soar-ir.repo.nii.ac.jp/record/11975/files/R-gottlieb-v12.pdf"}, "version_id": "ba9a9fd3-cf48-4ca2-8aff-f6b6346e08fb"}]}, "item_keyword": {"attribute_name": "\u30ad\u30fc\u30ef\u30fc\u30c9", "attribute_value_mlt": [{"subitem_subject": "evaluation subgroup", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Gottlieb group", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Whitehead product", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Sullivan model", "subitem_subject_scheme": "Other"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "journal article", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "A function space model approach to the rational evaluation subgroups", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "A function space model approach to the rational evaluation subgroups", "subitem_title_language": "en"}]}, "item_type_id": "6", "owner": "1", "path": ["1169/1170"], "permalink_uri": "http://hdl.handle.net/10091/1006", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2008-02-28"}, "publish_date": "2008-02-28", "publish_status": "0", "recid": "11975", "relation": {}, "relation_version_is_last": true, "title": ["A function space model approach to the rational evaluation subgroups"], "weko_shared_id": -1}