{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T18:29:53Z","timestamp":1793125793157,"version":"4.5.0"},"reference-count":53,"publisher":"International Press of Boston","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Differential Geom."],"published-print":{"date-parts":[[1982,1,1]]},"DOI":"10.4310\/jdg\/1214437136","type":"journal-article","created":{"date-parts":[[2017,3,16]],"date-time":"2017-03-16T11:05:38Z","timestamp":1489662338000},"page":"357-453","source":"Crossref","is-referenced-by-count":733,"title":["The topology of four-dimensional manifolds"],"prefix":"10.4310","volume":"17","author":[{"given":"Michael Hartley","family":"Freedman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2902","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[1] S. Armentrout, Cellular decompositions of 3-manifolds that yield 3-manifolds, Mem. Amer. Math. Soc. No. 107, 1970.","DOI":"10.1090\/memo\/0107"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] S. Akbulut and R. Kirby, Mazur manifolds, Michigan Math. J. 26 (1979) 259-284.","DOI":"10.1307\/mmj\/1029002261"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] J. J. Andrews and L. Rubin, Some spaces whose products with E is E 4, Bull. Amer. Math. Soc. 71 (1965) 675-677.","DOI":"10.1090\/S0002-9904-1965-11394-5"},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] R. J. Bean, Decompositions of E3 with a null sequence of starlike equivalent nondegenerate elements are E3, Illinois J. Math. 11 (1967), 21-23.","DOI":"10.1215\/ijm\/1256054779"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] R. H. Bing, Upper semicontinuous decompositions of E3, Ann. of Math. 65 (1957), 363-374.","DOI":"10.2307\/1969968"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] R. H. Bing, The cartesian product of a certain non-manifold and the line is E4, Ann. of Math. 70 (1959) 399-412.","DOI":"10.2307\/1970322"},{"key":"7","doi-asserted-by":"crossref","unstructured":"[7] W. Browder, Surgery on simply-connected manifolds, Ergebnisse Math, und ihrer Grenzgebiete, Vol. 65, Springer, Berlin, 1972.","DOI":"10.1007\/978-3-642-50020-6"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] W. Browder, J. Levine and G. Livesay, Finding a boundary for an open manifold, Amer. J. Math. 87 (1965) 1017-1028.","DOI":"10.2307\/2373259"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] M. Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960) 74-76.","DOI":"10.1090\/S0002-9904-1960-10400-4"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] M. Brown and H. Gluck, Stable structures on manifolds. I, II, III, Ann. of Math. 79 (1964) 1-58.","DOI":"10.2307\/1970481"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] J. Bryant and C. Seebeck, Locally nice imbeddings in codimension three, Quart. J. Math. Oxford Ser. 21 (1970) 265-272.","DOI":"10.1093\/qmath\/21.3.265"},{"key":"12","unstructured":"[12] S. Cappell, R. Lashof and J. Shaneson, A splitting theorem and the structure of 5-manifolds, 1st. Maz. Mat. Sympos. Mat. 10 (1972) 47-58."},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] S. Cappell and J. Shaneson, On topological knots and knot cobordism, Topology 12 (1973) 33-40.","DOI":"10.1016\/0040-9383(73)90020-7"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] S. Cappell and J. Shaneson, On four-dimensional surgery and applications, Comment. Math. Helv. 46 (1971) 500-528.","DOI":"10.1007\/BF02566862"},{"key":"15","unstructured":"[15] A. Casson, Three lectures on new infinite constructions in 4-dimensional manifolds, Notes prepared by L. Guillou, Prepublications Orsay 81 T 06."},{"key":"16","unstructured":"[16] J. Cerf, La nullite de o (Diff S 3), Seminaire H. Cartan, 1962\/63, Exp. 9, 10, 20, 21."},{"key":"17","doi-asserted-by":"crossref","unstructured":"[17] J. Cerf, La nullite de o (Diff S 3), Sur les diffeomorphismes de la sphere de dimension trois (4 = 0), Lecture Notes in Math. Vol. 53, Springer, Berlin, 1968.","DOI":"10.1007\/BFb0060395"},{"key":"18","unstructured":"[18] R. Edwards, The topology of manifolds and cell like maps, Proc. Intemat. Congress Math. Helsinki, 1978, 111-128."},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] R. Edwards, Dimension theory. I, Lecture Notes in Math. Vol. 438, Springer, Berlin, 1975, 195-211.","DOI":"10.1007\/BFb0066115"},{"key":"20","doi-asserted-by":"publisher","unstructured":"[20] R. Edwards and R. Kirby, Deformations of spaces imbeddings, Ann. of Math. 93 (1971), 63-88.","DOI":"10.2307\/1970753"},{"key":"21","unstructured":"[21] F. Farrel and J. Wagnor, Lecture on a proof of the proper-h-cobordism theorem, University of California, Berkeley, 1972."},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] M. H. Freedman, A fake S 3 X R, Ann. of Math. 110 (1979) 177-201.","DOI":"10.2307\/1971257"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] M. H. Freedman, A fake S 3 X R, A surgery sequence in dimension four, the relations with knot concordance, Invent. Math., to appear.","DOI":"10.1007\/BF01394055"},{"key":"24","doi-asserted-by":"crossref","unstructured":"[24] M. H. Freedman and R. Kirby, A geometric proof of Rochlin's theorem, Proc. Sympos. Pure Math. Vol. 32, Part 2, 1978, 85-98.","DOI":"10.1090\/pspum\/032.2\/520525"},{"key":"25","doi-asserted-by":"publisher","unstructured":"[25] M. H. Freedman and F. Quinn, Slightly singular 4-manifolds, Topology 20 (1981) 161-173.","DOI":"10.1016\/0040-9383(81)90035-5"},{"key":"26","doi-asserted-by":"publisher","unstructured":"[26] D. Galewski and R. Stern, Classification of simplicial triangulations of topological manifolds, Ann. of Math. III (1980) 1-34.","DOI":"10.2307\/1971215"},{"key":"27","unstructured":"[27] M. Hirsh and B. Mazur, Smoothing piecewise linear manifolds, Annals of Math. Studies No. 80, Princeton University Press, Princeton, 1974."},{"key":"28","unstructured":"[28] T. Homma, On the imbedding of polyhedra into manifolds, Yokohama Math. J. 10 (1962) 5-10."},{"key":"29","doi-asserted-by":"publisher","unstructured":"[29] R. Kirby, On the set of nonlocally flat points of a submanifold of codimension one, Ann. of Math. 88 (1968) 281-290.","DOI":"10.2307\/1970575"},{"key":"30","doi-asserted-by":"publisher","unstructured":"[30] R. Kirby, A calculus for framed links in S 3, Invent. Math. 45 (1978) 35-56.","DOI":"10.1007\/BF01406222"},{"key":"31","doi-asserted-by":"crossref","unstructured":"[31] R. Kirby and M. Scharlemann, Eight faces of the Poincare homology 3-sphere, Geometric Topology, edited by J. C. Cantrell (Athens, Georgia 1979), Academic Press, New York, 1979, 113-146.","DOI":"10.1016\/B978-0-12-158860-1.50015-0"},{"key":"32","doi-asserted-by":"publisher","unstructured":"[32] R. Kirby and L. Siebenmann, On the triangulation of manifolds and the Haupermutung, Bull. Amer. Math. Soc. 75 (1969) 742-749.","DOI":"10.1090\/S0002-9904-1969-12271-8"},{"key":"33","doi-asserted-by":"crossref","unstructured":"[33] R. Kirby and L. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Annals of Math. Studies No. 88, Princeton University Press, Princeton, 1977.","DOI":"10.1515\/9781400881505"},{"key":"34","doi-asserted-by":"crossref","unstructured":"[34] F. Laudenbath, Sur les 2-spheres d'une ariete de dimension 3, Ann. of Math. 97 (1973) 57-81.","DOI":"10.2307\/1970877"},{"key":"35","doi-asserted-by":"publisher","unstructured":"[35] D. R. McMillan, A criterion for cellularity in a manifold, Ann. of Math. 79 (1964) 327-337.","DOI":"10.2307\/1970548"},{"key":"36","unstructured":"[36] J. Milnor, On simply connected 4-manifolds, Internat. Sympos. on Algebraic Topology, 1958, 122-128."},{"key":"37","doi-asserted-by":"crossref","unstructured":"[37] J. Milnor, Lectures on the h-cobordism theorem, Math. Notes, Princeton University Press, Princeton, 1965.","DOI":"10.1515\/9781400878055"},{"key":"38","doi-asserted-by":"publisher","unstructured":"[38] E. Moise, Affine structures on 3-manifolds, Ann. of Math. 56 (1952) 96-114.","DOI":"10.2307\/1969769"},{"key":"39","unstructured":"[39] J. R. Munkres, Elementary differential topology, Annals of Math. Studies, No. 54, Princeton University Press, Princeton, 1961."},{"key":"40","doi-asserted-by":"publisher","unstructured":"[40] R. A. Norman, Dehn's lemma for certain 4-manifolds, Invent. Math. 7 (1969) 143-147.","DOI":"10.1007\/BF01389797"},{"key":"41","doi-asserted-by":"publisher","unstructured":"[41] F. Quinn, Ends of maps, Ann. of Math. 110 (1979) 275-331.","DOI":"10.2307\/1971262"},{"key":"42","unstructured":"[42] D. Rolfsen, Knots and links, Publish or Perish, Boston, 1976."},{"key":"43","doi-asserted-by":"publisher","unstructured":"[43] M. Scharlemann, Transversality theories at dimension 4, Invent. Math. 33 (1976) 1-14.","DOI":"10.1007\/BF01425502"},{"key":"44","unstructured":"[44] L. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension ^ 5, Ph. D. Thesis, Princeton University, Princeton, 1965."},{"key":"45","unstructured":"[45] L. Siebenmann, Disruption of low-dimensional handle body theory by Rochlin's theorem. Topology of Manifolds, edited by J. C. Cantrell and C. H. Edwards (Athens, Georgia Conf. 1969), Markham, Chicago, 1970, 57-76."},{"key":"46","doi-asserted-by":"crossref","unstructured":"[46] L. Siebenmann, Infinite simple homotopy types, Indag. Math. 32 (1970) 479-495.","DOI":"10.1016\/S1385-7258(70)80052-X"},{"key":"47","doi-asserted-by":"publisher","unstructured":"[47] L. Siebenmann, Approximating cellular maps by homeomorphisms, Topology 11(1973) 271-294.","DOI":"10.1016\/0040-9383(72)90014-6"},{"key":"48","unstructured":"[48] L. Siebenmann, Seminaire Bourbaki, 1982, Exp. 588, 1-30."},{"key":"49","doi-asserted-by":"publisher","unstructured":"[49] S. Smale, Diffeomorphisms of the 2-sphere, Proc. Amer. Math. Soc. 10 (1959) 621-626.","DOI":"10.2307\/2033664"},{"key":"50","doi-asserted-by":"publisher","unstructured":"[50] S. Smale, Generalized Poincare's conjecture in dimensions > 4, Ann. of Math. 74 (1961) 391-466.","DOI":"10.2307\/1970239"},{"key":"51","unstructured":"[51] L. Taylor, Doctoral dissertation, University of California, Berkeley, 1972."},{"key":"52","unstructured":"[52] C. T. C. Wall, Surgery on compact manifolds, Academic Press, New York, 1971."},{"key":"53","doi-asserted-by":"crossref","unstructured":"[53] J. H. C. Whitehead, A certain open manifold whose group is unity, Quart. J. Math. Oxford Ser. 6 (1935) 268-279.","DOI":"10.1093\/qmath\/os-6.1.268"}],"container-title":["Journal of Differential Geometry"],"original-title":[],"deposited":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T18:01:16Z","timestamp":1792173676000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/journal-of-differential-geometry\/volume-17\/issue-3\/The-topology-of-four-dimensional-manifolds\/10.4310\/jdg\/1214437136.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,1,1]]},"references-count":53,"journal-issue":{"issue":"3","published-online":{"date-parts":[[1982,1,1]]}},"URL":"https:\/\/doi.org\/10.4310\/jdg\/1214437136","relation":{},"ISSN":["0022-040X"],"issn-type":[{"value":"0022-040X","type":"print"}],"subject":[],"published":{"date-parts":[[1982,1,1]]}}}