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The homology of MSpin

Published online by Cambridge University Press:  24 October 2008

V. Giambalvo
Affiliation:
University of Connecticut and New Mexico State University
David J. Pengelley
Affiliation:
University of Connecticut and New Mexico State University

Extract

The mod two homology of MSpin, the Spin-cobordism Thom spectrum, has a rich algebraic structure. We will describe it explicitly as a comodule algebra, and give some applications to the ring structure of the Spin-cobordism ring.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Adams, J. F. and Priddy, S. B.. Uniqueness of BSO. Math. Proc. Cambridge Philos. Soc. 80 (1976), 475509.CrossRefGoogle Scholar
[2]Anderson, D. W., Brown, E. H. and Peterson, F. P.. The structure of the Spin-cobordism ring. Ann. of Math. 86 (1967), 271298.CrossRefGoogle Scholar
[3]Bahri, A. P. and Mahowald, M. E.. A direct summand in H*(MO〈8〉 Z 2). Proc. Amer. Math. Soc. 78 (1980), 295298.Google Scholar
[4]Davis, D. M.. On the cohomology of MO〈8〉. Proc. Symposium on Algebraic Topology in Honor of Jose Adem. Contemporary Mathematics 12 (1982), 91104. Amer. Math. Soc.CrossRefGoogle Scholar
[5]Davis, D. M. and Mahowald, M.. Ext over the subalgebra A 2 of the Steenrod algebra for stunted projective spaces. Proc. Conf., Current Trends in Algebraic Topology, Canadian Math. Soc. Conf. Proc. 2, part 1 (1982), 297342. Amer. Math. Soc.Google Scholar
[6]Milnor, J. W. and Moore, J. C.. On the structure of Hopf algebras. Ann. of Math. 81 (1965), 211264.CrossRefGoogle Scholar
[7]Pengelley, D. J.. The homotopy type of MSU. Amer. J. Math. 104 (1982), 11011123.CrossRefGoogle Scholar
[8]Pengelley, D. J.. The A-algebra structure of Thorn spectra: MSO as an example. Proc.Conf., Current Trends in Algebraic Topology, Canadian Math. Soc. Conf. Proc. 2, part 1 (1982), 5110–513. Amer. Math. Soc.Google Scholar
[9]Pengelley, D. J.. H*(MO〈8〉 Z/2) is an extended A 2*-coalgebra. Proc. Amer. Math. Soc. 87 (1983), 355356.Google Scholar
[10]Pengelley, D. J.. The mod two homology of MSO and MSU as A-comodule algebras, and the cobordism ring. J. London Math. Soc. (2), 25 (1982), 467472.CrossRefGoogle Scholar
[11]Stong, R. E.. Notes on Cobordism Theory. (Princeton University Press, 1968).Google Scholar