Skeleta of complexes with low 𝑀𝑈_{∗} projective dimension

Johnson, David Copeland

doi:10.1090/S0002-9939-1972-0288754-1

Skeleta of complexes with low $MU_\ast$ projective dimension
HTML articles powered by AMS MathViewer

by David Copeland Johnson PDF

Proc. Amer. Math. Soc. 32 (1972), 599-604 Request permission

Abstract:

Let $M{U_ \ast }(X)$ be the unitary bordism of a finite complex X. Let ${X^p}$ be the p-skeleton of X. This note proves that certain properties of $M{U_ \ast }(X)$ are shared by $M{U_\ast }({X^p})$ when the projective dimension of $M{U_\ast }(X)$ as a $M{U_\ast }$ module is low (0, 1, or 2).

References

J. F. Adams, On Chern characters and the structure of the unitary group, Proc. Cambridge Philos. Soc. 57 (1961), 189–199. MR 121795, DOI 10.1017/s0305004100035052
P. E. Conner and E. E. Floyd, The relation of cobordism to $K$-theories, Lecture Notes in Mathematics, No. 28, Springer-Verlag, Berlin-New York, 1966. MR 0216511, DOI 10.1007/BFb0071091
P. E. Conner and Larry Smith, On the complex bordism of finite complexes, Inst. Hautes Études Sci. Publ. Math. 37 (1969), 117–221. MR 267571, DOI 10.1007/BF02684888
Albrecht Dold, On general cohomology. Chapters 1–9, Aarhus Universitet, Matematisk Institut, Aarhus, 1968. Lectures given at the Nordic Summer School in Mathematics (June 16th-July 6th, 1968). MR 0254838
David Copeland Johnson and Larry Smith, On the relation of complex cobordism to connective $K$-theory, Proc. Cambridge Philos. Soc. 70 (1971), 19–22. MR 293619, DOI 10.1017/s0305004100049616
Peter S. Landweber, On the complex bordism and cobordism of infinite complexes, Bull. Amer. Math. Soc. 76 (1970), 650–654. MR 258021, DOI 10.1090/S0002-9904-1970-12476-4

Homology

28

Larry Smith, On the relation of connective $K$-theory to homology, Proc. Cambridge Philos. Soc. 68 (1970), 637–639. MR 263072, DOI 10.1017/s0305004100076623

A note on the Hattori-Stong theorem

Rainer Vogt, Boardman’s stable homotopy category, Lecture Notes Series, No. 21, Aarhus Universitet, Matematisk Institut, Aarhus, 1970. MR 0275431