{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T19:50:11Z","timestamp":1773258611176,"version":"3.50.1"},"reference-count":28,"publisher":"AIP Publishing","issue":"9","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2007,9,1]]},"abstract":"<jats:p>We define an invariant of graphs embedded in a 3-manifold and a partition function for 2-complexes embedded in a triangulated 4-manifold by specifying the values of variables in the Turaev-Viro and Crane-yetter state-sum models. In the case of the three-dimensional invariant, we prove a duality formula relating its Fourier transform to another invariant defined via the colored Jones polynomial. In the case of the four-dimensional partition function, we give a formula for it in terms of a regular neighborhood of the 2-complex and the signature of its complement. Some examples are computed which show that the partition function determines an invariant which can detect non locally-flat surfaces in a 4-manifold.<\/jats:p>","DOI":"10.1063\/1.2759440","type":"journal-article","created":{"date-parts":[[2007,9,20]],"date-time":"2007-09-20T14:46:48Z","timestamp":1190299608000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":24,"title":["Observables in the Turaev-Viro and Crane-Yetter models"],"prefix":"10.1063","volume":"48","author":[{"given":"John W.","family":"Barrett","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences , University Park, Nottingham NG7 2RD, UK"}]},{"given":"Jo\u00e3o","family":"Faria Martins","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico Departamento de Matem\u00e1tica, , Av. Rovisco Pais, 1049-001 Lisboa, Portugal and Departamento de Matem\u00e1tica, Universidade Lus\u00f3fona de Humanidades e Tecnologia, Av do Campo Grande, 376, 1749-024, Lisboa, Portugal"}]},{"given":"J. Manuel","family":"Garc\u00eda-Islas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas , CINVESTAV, Apartado Postal 14-740, 07000, Mexico, D.F., Mexico"}]}],"member":"317","published-online":{"date-parts":[[2007,9,19]]},"reference":[{"key":"2023080221462129200_c1","first-page":"97","volume":"18","year":"2003","journal-title":"Int. J. Mod. Phys. A"},{"key":"2023080221462129200_c2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1088\/0264-9381\/23\/1\/008","volume":"23","year":"2006","journal-title":"Class. 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