{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T14:37:46Z","timestamp":1716907066762},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,5]]},"abstract":"<jats:p> For a torus bundle (S<jats:sup>1<\/jats:sup> \u00d7 S<jats:sup>1<\/jats:sup>) \u2192 M \u2192 S<jats:sup>1<\/jats:sup>, we construct a finite free resolution of \u2124 over \u2124[\u03c0<jats:sub>1<\/jats:sub>(M)] and compute the cohomology groups H*(\u03c0<jats:sub>1<\/jats:sub>(M); \u2124) and H*(\u03c0<jats:sub>1<\/jats:sub>(M);\u2124<jats:sub>p<\/jats:sub>) for a prime p. We also construct a partial diagonal approximation for the resolution, which allows us to compute the cup products in H*(\u03c0<jats:sub>1<\/jats:sub>(M); \u2124) and H*(\u03c0<jats:sub>1<\/jats:sub>(M); \u2124<jats:sub>p<\/jats:sub>). <\/jats:p>","DOI":"10.1142\/s0218196715500071","type":"journal-article","created":{"date-parts":[[2015,2,12]],"date-time":"2015-02-12T02:40:57Z","timestamp":1423708857000},"page":"493-530","source":"Crossref","is-referenced-by-count":2,"title":["Diagonal approximation and the cohomology ring of torus fiber bundles"],"prefix":"10.1142","volume":"25","author":[{"given":"S\u00e9rgio Tadao","family":"Martins","sequence":"first","affiliation":[{"name":"Department of Mathematics \u2014 IME, University of S\u00e3o Paulo, Rua do Mat\u00e3o, 1010 \u2014 05508\u2013090, S\u00e3o Paulo \u2014 SP, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2015,4,9]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-06280-7"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9327-6"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(99)00062-0"},{"key":"rf5","unstructured":"D. L.\u00a0Gon\u00e7alves, C.\u00a0Hayat and P.\u00a0Zvengrowki, Group Actions and Homogeneous Spaces, eds. J.\u00a0Korba\u0161, M.\u00a0Morimoto and K.\u00a0Pawalowski (Fak. Mat. Fyziky Inform. Univ. Komensk\u00e9ho, Bratislava, 2010)\u00a0pp. 9\u201328."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2748\/tmj\/1178225952"},{"key":"rf7","series-title":"Annals of Mathematical Studies","volume-title":"3-Manifolds","volume":"86","author":"Hempel J.","year":"1976"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972713000877"},{"key":"rf9","unstructured":"J.\u00a0Stallings, Topology of 3-manifolds and related topics (Prentice-Hall, Englewood Cliffs, N.J., 1962)\u00a0pp. 95\u2013100."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.2140\/gtm.2008.14.519"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100035155"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196715500071","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T04:04:44Z","timestamp":1565150684000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196715500071"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,9]]},"references-count":10,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2015,4,9]]},"published-print":{"date-parts":[[2015,5]]}},"alternative-id":["10.1142\/S0218196715500071"],"URL":"https:\/\/doi.org\/10.1142\/s0218196715500071","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,9]]}}}