{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T20:20:37Z","timestamp":1743020437829,"version":"3.40.3"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030779566"},{"type":"electronic","value":"9783030779573"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-77957-3_9","type":"book-chapter","created":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T22:02:27Z","timestamp":1624744947000},"page":"154-178","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Relevant Differential Topology in Statistical Manifolds"],"prefix":"10.1007","author":[{"given":"Michel","family":"Nguiffo-Boyom","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,27]]},"reference":[{"key":"9_CR1","series-title":"Lecture Notes in Statistics","volume-title":"Geometrical Methods in Statistics","author":"I-S Amari","year":"1990","unstructured":"Amari, I.-S.: Geometrical Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer, New York (1990)"},{"key":"9_CR2","unstructured":"Amari, I.-S., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs, vol. 191. AMS-OXFORD (2000)"},{"key":"#cr-split#-9_CR3.1","doi-asserted-by":"crossref","unstructured":"Cartan, E.: Sur les vari\u00e9t\u00e9s \u00e0 coonexions affines et la th\u00e9orie de relativit\u00e9 g\u00e9n\u00e9rals\u00e9e. Ann. Sci. Ec. Norm. Sup. (1) 40, 325-412 (1923)","DOI":"10.24033\/asens.751"},{"key":"#cr-split#-9_CR3.2","unstructured":"(2) 40, 1-25 (1924). (3) 42, 17-88 (1925)"},{"key":"9_CR4","unstructured":"Ghys, E.: How to construct all Riemannian foliations, in Molino\u2019s, Riemnnian foliations, Appendix"},{"key":"9_CR5","unstructured":"Gromov, M.: The search of structures: (i) ECM6, KRAKOW 2012, (ii) MaxEnt 2014. Proc. Amer Soc Phys (2013)"},{"key":"9_CR6","first-page":"544","volume":"116","author":"V Guillemin","year":"1965","unstructured":"Guillemin, V.: The integrability problem for G-structures. Trans. Am. Math. Soc. 116, 544\u2013560 (1965)","journal-title":"Trans. Am. Math. Soc."},{"key":"9_CR7","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1090\/S0002-9904-1964-11019-3","volume":"70","author":"V Guillemin","year":"1964","unstructured":"Guillemin, V., Sternberg, S.: An algebraic model for transitive differential geometry. Bull. Am. Math. Soc. 70, 16\u201347 (1964)","journal-title":"Bull. Am. Math. Soc."},{"key":"9_CR8","doi-asserted-by":"crossref","unstructured":"Hochschild, G., Serre, J.P.: Cohomology of group extensions. Trans. Amer Math Soc. 74(1), 110\u2013134 (1953)","DOI":"10.1090\/S0002-9947-1953-0052438-8"},{"key":"9_CR9","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/BF02411907","volume":"43","author":"S Kobayashi","year":"1957","unstructured":"Kobayashi, S.: The theory of connections. Annali di Matematica 43, 119\u2013194 (1957)","journal-title":"Annali di Matematica"},{"key":"9_CR10","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/BF02787690","volume":"15","author":"I Singer","year":"1965","unstructured":"Singer, I., Sternberg, S.: The infinte groups of Lie and Cartan. J. Analyse Math. 15, 114 (1965)","journal-title":"J. Analyse Math."},{"key":"9_CR11","unstructured":"Koszul, J.-L.: Sur les deformations des varietes localement plates"},{"key":"9_CR12","unstructured":"Sur l\u2019homologie des formes diff?rentielles d\u2019ordre superieur"},{"key":"9_CR13","unstructured":"Lichnerowicz, Theorie globale des connexions et des groupes d\u2019holonomie. Edizioni Cremonese (1962)"},{"key":"9_CR14","doi-asserted-by":"crossref","unstructured":"Lyndon, R.C.: The conhomology of group extensions. Duke Math. J. 15(1), 271\u2013292 (1948)","DOI":"10.1215\/S0012-7094-48-01528-2"},{"issue":"5","key":"9_CR15","first-page":"1225","volume":"30","author":"P MacCullagh","year":"2002","unstructured":"MacCullagh, P.: What is a statistical model. Ann. Stat. 30(5), 1225\u20131310 (2002)","journal-title":"Ann. Stat."},{"key":"9_CR16","doi-asserted-by":"crossref","unstructured":"Moerdijk, I., Mrcun, J.: Introduction to Foliations and Lie groupoids. Cambridge Studies in Advanced Mathematics, vol. 91 (2003)","DOI":"10.1017\/CBO9780511615450"},{"key":"9_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-8670-4","volume-title":"Riemannian Foliations","author":"P Molino","year":"1988","unstructured":"Molino, P.: Riemannian Foliations. Birkhauser, Boston (1988)"},{"key":"9_CR18","unstructured":"Murray, M.K., Rice, J.W.: Differential Geometry and Statistics. Monographs on Statistics and Applied Probability, vol. 48. Chapman-Hall CRC, London (1993)"},{"key":"9_CR19","doi-asserted-by":"crossref","unstructured":"Nguiffo Boyom, M.: Foliation-web-heessian geometry-information geometry-enropy and cohomology. Entropy 18(12), 433 (2016)","DOI":"10.3390\/e18120433"},{"key":"9_CR20","unstructured":"Nguiffo Boyom, M.: The last formula of Koszul. J. Inf. Geom. (2019). https:\/\/doi.org\/10.10071-48"},{"key":"9_CR21","unstructured":"Nguiffo Boyom, M.: New Invariants and Old open Problems in the quantitative Global Analysis (preprint)"},{"key":"9_CR22","doi-asserted-by":"crossref","unstructured":"Palais, R.: A global formulation of the lie theory of transformation groups. Mem. Am. Math. Soc. 22 (1957)","DOI":"10.1090\/memo\/0022"},{"key":"9_CR23","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1090\/S0002-9939-1961-0123638-3","volume":"12","author":"RS Palais","year":"1961","unstructured":"Palais, R.S., Stewart, T.E.: Torus bandle over torus. Proc. Am. Math. Soc. 12, 26\u201340 (1961)","journal-title":"Proc. Am. Math. Soc."},{"key":"9_CR24","doi-asserted-by":"crossref","unstructured":"Reihnardt, B.L.: Foliated manifolds with bundlelike metrics. Ann. Math. 69(2), 119\u20131329 (1959)","DOI":"10.2307\/1970097"},{"key":"9_CR25","volume-title":"The Differential Geometry of Hessian Manifolds","author":"H Shima","year":"2007","unstructured":"Shima, H.: The Differential Geometry of Hessian Manifolds. World Scientific Publishing, Hackensack (2007)"},{"key":"9_CR26","volume-title":"Spaces of Constant Curvature","author":"J Wolf","year":"1974","unstructured":"Wolf, J.: Spaces of Constant Curvature. Publish of Perish, Boston (1974)"}],"container-title":["Springer Proceedings in Mathematics &amp; Statistics","Geometric Structures of Statistical Physics, Information Geometry, and Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-77957-3_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T22:04:33Z","timestamp":1624745073000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-77957-3_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030779566","9783030779573"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-77957-3_9","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"27 June 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SPIGL","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Workshop on Joint Structures and Common Foundations of Statistical Physics, Information Geometry and Inference for Learning","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Les Houches","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 July 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31 July 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"spigl2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/franknielsen.github.io\/SPIG-LesHouches2020\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}