×

On manifolds representing homology classes in codimension 2. (English) Zbl 0283.57018


MSC:

57R95 Realizing cycles by submanifolds
57N35 Embeddings and immersions in topological manifolds
57P10 Poincaré duality spaces
57R20 Characteristic classes and numbers in differential topology
57R65 Surgery and handlebodies
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Andreotti, A., Frankel, T.: The Lefschetz theorem on hyperplane sections. Ann. of Math.69, 713-717 (1959) · Zbl 0115.38405
[2] Atiyah, M., Singer, I.: The index of elliptic operators: III. Ann. of Math87, 546-604 (1968) · Zbl 0164.24301
[3] Borel, A.: Seminar on transformation groups. Ann. of Math. studies46, Princeton 1960 · Zbl 0091.37202
[4] Bott, R.: On a theorem of Lefschetz. Mich, Math. J.,6, 211-216 (1959) · Zbl 0113.36502
[5] Bott, R.: The stable homotopy of the classical groups. Ann. of Math.70, 313-337 (1959) · Zbl 0129.15601
[6] Bourbaki, N.: Algèbre. Chapitre 6, 7, 2e ed., Paris: Hermann 1964 · Zbl 0205.34302
[7] Bourbaki, N.: Algèbre. Chapitre 9. Paris: Hermann 1959 · Zbl 0102.25503
[8] Browder, W.: Structures onM{\(\times\)}R: Proc. Comb. Phil. Soc.67, 337-345 (1965) · Zbl 0129.39201
[9] Freedman, M.: Codimension-2 Surgery. Princeton thesis, 1973. · Zbl 0369.57012
[10] Hardy, G. H., Wright, E. M.: An introduction to the theory of numbers. 3rd ed., New York: Oxford University Press 1966 · Zbl 0020.29201
[11] Hirzebruch, F.: Topological methods in algebraic geometry 3rd ed., Berlin-Heidelberg-New York: Springer 1966 · Zbl 0138.42001
[12] Hirzebruch, F.: The signature of ramified converings. In: Global Analysis. Papers in honor of Kodaira, pp. 253-265. Princeton: Princeton University Press 1969
[13] Hsiang, W., Szczarba, R.: On embedding surfaces in 4-manifolds Proc. of Symp. in Pure Math. XXII. Algebraic Topology, 97-103 (1971)
[14] Jänich, K., Ossa, E.: On the signature of an involution. Topology8 27-30 (1969) · Zbl 0184.27302
[15] Jordan, C.: Calculus of finite differences. New York: Chelsea 1960 · Zbl 0060.12309
[16] Jupp, P.: Classification of certain 6-manifolds. Proc. Camb. Phil. Soc.73, 293-300 (1973) · Zbl 0249.57005
[17] Kato, M., Matsumoto, Y.: Simply connected surgery of submanifolds in codimension two, I. J. Math. Soc. Japan24, 586-608 (1972) · Zbl 0238.57018
[18] Kervaire, M., Milnor, J.: Bernoulli numbers, homotopy groups and a theorem of Rohlin. Proc. Internat. Congress Math. 454-458 (1958)
[19] Kervaire, M., Milnor, J.: On 2-spheres in 4-manifolds. PNAS47, 1651-1657 (1961) · Zbl 0107.40303
[20] Massey, W. S.: Proof of a conjecture of Whitney. Pacific J. Math.31, 143-156 (1969) · Zbl 0198.56701
[21] Milnor, J.: On simply connected 4-manifolds. International symposium on algebraic topology, p. 122-128. Mexico City: Univ. Nacional Automata de México 1958
[22] Milnor, J.: Morse Theory. Ann. of Math. studies51, Princeton, 1963
[23] Nielsen, N.: Traité élémentaire des nombres de Bernoulli. Paris 1923. · JFM 50.0170.04
[24] Quinn, F.: Almost canonical inverse images. (To appear in Comm. Math. Helv.)
[25] Rokhlin, V. A.: Two-dimensional submanifolds of four-dimensional manifolds. Functional Analysis and Its Applications5, 39-48 (1971) · Zbl 0268.57019
[26] Shafarevich, I. R.: Foundations of algebraic geometry. Russian Math. Surveys,24, No. 6, 1-178 (1969) · Zbl 0204.21301
[27] Spanier, E.: Algebraic Topology. New York: McGraw Hill 1966 · Zbl 0145.43303
[28] Spanier, E.: The homotopy excision theorem. Mich. J. Math.14, 245-255 (1967) · Zbl 0148.17002
[29] Thom, R.: Quelques propriétés globales des variétés differentiables. Comm. Math. Helv.28, 17-86 (1954) · Zbl 0057.15502
[30] Thomas, E., Wood, J.: On signatures associated with ramified coverings and embedding problems. Ann. Inst. Fourier23, 229-235 (1973) · Zbl 0262.57012
[31] Wall, C. T. C.: On simply-connected 4-manifolds. J. London Math. Soc.39, 141-149 (1964) · Zbl 0131.20701
[32] Wall, C. T. C.: Classification problems in differential topology. V. On certain 6-manifolds. Inventiones math.1, 355-374 (1966) · Zbl 0149.20601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.