Generators for the bordism algebra of immersions
HTML articles powered by AMS MathViewer
- by M. A. Aguilar PDF
- Trans. Amer. Math. Soc. 316 (1989), 39-51 Request permission
Abstract:
Let us denote by $I(n,k)$ the group of bordism classes of immersions of closed smooth $n$-manifolds in closed smooth $(n + k)$-manifolds $(k > 0)$. We can make $I({\ast },k)$ into a graded algebra over the unoriented bordism ring. This algebra is polynomial. In this paper we give two sets of immersions which are polynomial generators.References
- John Frank Adams, Infinite loop spaces, Annals of Mathematics Studies, No. 90, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1978. MR 505692 R. M. Alliston, Dyer-Lashof operations and bordism, Ph. D. Thesis. Univ. of Virginia, 1976.
- Theodor Bröcker and Tammo tom Dieck, Kobordismentheorie, Lecture Notes in Mathematics, Vol. 178, Springer-Verlag, Berlin-New York, 1970 (German). MR 0275446
- William Browder, Homology operations and loop spaces, Illinois J. Math. 4 (1960), 347–357. MR 120646
- Frederick R. Cohen, Thomas J. Lada, and J. Peter May, The homology of iterated loop spaces, Lecture Notes in Mathematics, Vol. 533, Springer-Verlag, Berlin-New York, 1976. MR 0436146
- P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478
- P. E. Conner and E. E. Floyd, Fibring within a cobordism class, Michigan Math. J. 12 (1965), 33–47. MR 179796
- Eldon Dyer and R. K. Lashof, Homology of iterated loop spaces, Amer. J. Math. 84 (1962), 35–88. MR 141112, DOI 10.2307/2372804
- Daniel S. Kahn and Stewart B. Priddy, On the transfer in the homology of symmetric groups, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 91–101. MR 464229, DOI 10.1017/S0305004100054323
- J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609
- J. Milnor, On the Stiefel-Whitney numbers of complex manifolds and of spin manifolds, Topology 3 (1965), 223–230. MR 180977, DOI 10.1016/0040-9383(65)90055-8
- Helmut Schulte-Croonenberg, Dyer-Lashof-Operationen in Bordismustheorien, Pahl-Rugenstein-Hochschulschriften Gesellschafts- und Naturwissenschaften, Serie: Mathematik [Pahl-Rugenstein University Texts in the Social and Natural Sciences, Series: Mathematics], vol. 62, Pahl-Rugenstein Verlag, Cologne, 1981 (German). With an English summary. MR 645357
- Paul A. Schweitzer, Joint cobordism of immersions, The Steenrod Algebra and its Applications (Proc. Conf. to Celebrate N. E. Steenrod’s Sixtieth Birthday, Battelle Memorial Inst., Columbus, Ohio, 1970) Lecture Notes in Mathematics, Vol. 168, Springer, Berlin, 1970, pp. 267–282. MR 0278322
- Robert M. Switzer, Algebraic topology—homotopy and homology, Die Grundlehren der mathematischen Wissenschaften, Band 212, Springer-Verlag, New York-Heidelberg, 1975. MR 0385836
- René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923
- Tammo tom Dieck, Steenrod-Operationen in Kobordismen-Theorien, Math. Z. 107 (1968), 380–401 (German). MR 244989, DOI 10.1007/BF01110069
- C. T. C. Wall, Cobordism of pairs, Comment. Math. Helv. 35 (1961), 136–145. MR 124913, DOI 10.1007/BF02567012
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 316 (1989), 39-51
- MSC: Primary 57R90; Secondary 57R42
- DOI: https://doi.org/10.1090/S0002-9947-1989-0979961-8
- MathSciNet review: 979961