{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1360294646567950592.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1090/s0002-9947-2012-05732-1"}},{"identifier":{"@type":"URI","@value":"http://www.ams.org/tran/2013-365-06/S0002-9947-2012-05732-1/S0002-9947-2012-05732-1.pdf"}},{"identifier":{"@type":"URI","@value":"https://www.ams.org/tran/2013-365-06/S0002-9947-2012-05732-1/S0002-9947-2012-05732-1.pdf"}}],"dc:title":[{"@value":"Kreck-Stolz invariants for quaternionic line bundles"}],"description":[{"type":"abstract","notation":[{"@value":"<p>\n                    We generalise the Kreck-Stolz invariants\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"s 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>s</mml:mi>\n                            <mml:mn>2</mml:mn>\n                          </mml:msub>\n                          <mml:annotation encoding=\"application/x-tex\">s_2</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    and\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"s 3\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>s</mml:mi>\n                            <mml:mn>3</mml:mn>\n                          </mml:msub>\n                          <mml:annotation encoding=\"application/x-tex\">s_3</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    by defining a new invariant, the\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t\">\n                        <mml:semantics>\n                          <mml:mi>t</mml:mi>\n                          <mml:annotation encoding=\"application/x-tex\">t</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    -invariant, for quaternionic line bundles \n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\">\n                        <mml:semantics>\n                          <mml:mi>E</mml:mi>\n                          <mml:annotation encoding=\"application/x-tex\">E</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    over closed spin-manifolds\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\">\n                        <mml:semantics>\n                          <mml:mi>M</mml:mi>\n                          <mml:annotation encoding=\"application/x-tex\">M</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    of dimension\n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"4 k minus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>4</mml:mn>\n                            <mml:mi>k</mml:mi>\n                            <mml:mo>\n                              −\n                              \n                            </mml:mo>\n                            <mml:mn>1</mml:mn>\n                          </mml:mrow>\n                          <mml:annotation encoding=\"application/x-tex\">4k-1</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    with \n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H cubed left-parenthesis upper M semicolon double-struck upper Q right-parenthesis equals 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>H</mml:mi>\n                              <mml:mn>3</mml:mn>\n                            </mml:msup>\n                            <mml:mo stretchy=\"false\">(</mml:mo>\n                            <mml:mi>M</mml:mi>\n                            <mml:mo>;</mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\n                            </mml:mrow>\n                            <mml:mo stretchy=\"false\">)</mml:mo>\n                            <mml:mo>=</mml:mo>\n                            <mml:mn>0</mml:mn>\n                          </mml:mrow>\n                          <mml:annotation encoding=\"application/x-tex\">H^3(M; \\mathbb Q) = 0</mml:annotation>\n                        </mml:semantics>\n                      </mml:math>\n                    </inline-formula>\n                    such that \n                    <inline-formula content-type=\"math/mathml\">\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML ..."}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1380294646567950593","@type":"Researcher","foaf:name":[{"@value":"Diarmuid Crowley"}]},{"@id":"https://cir.nii.ac.jp/crid/1380294646567950592","@type":"Researcher","foaf:name":[{"@value":"Sebastian Goette"}]}],"publication":{"publicationIdentifier":[{"@type":"EISSN","@value":"10886850"},{"@type":"PISSN","@value":"00029947"}],"prism:publicationName":[{"@value":"Transactions of the American Mathematical Society"}],"dc:publisher":[{"@value":"American Mathematical Society (AMS)"}],"prism:publicationDate":"2012-11-20","prism:volume":"365","prism:number":"6","prism:startingPage":"3193","prism:endingPage":"3225"},"reviewed":"false","dc:rights":["https://www.ams.org/publications/copyright-and-permissions"],"url":[{"@id":"http://www.ams.org/tran/2013-365-06/S0002-9947-2012-05732-1/S0002-9947-2012-05732-1.pdf"},{"@id":"https://www.ams.org/tran/2013-365-06/S0002-9947-2012-05732-1/S0002-9947-2012-05732-1.pdf"}],"createdAt":"2012-11-20","modifiedAt":"2026-03-11","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/2051433317034804992","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Some comments on 6D global gauge anomalies"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1090/s0002-9947-2012-05732-1"},{"@type":"CROSSREF","@value":"10.1093/ptep/ptab015_references_DOI_9duH8hKX6ALblmBe7C8kMe1innl"}]}