Morava $K$-theory and the free loop space
HTML articles powered by AMS MathViewer
- by John McCleary and Dennis A. McLaughlin
- Proc. Amer. Math. Soc. 114 (1992), 243-250
- DOI: https://doi.org/10.1090/S0002-9939-1992-1079897-6
- PDF | Request permission
Abstract:
We generalize a result of Hopkins, Kuhn, and Ravenel relating the $n$ th Morava $K$-theory of the free loop space of a classifying space of a finite group to the $(n + 1)$ st Morava $K$-theory of the space. We show that the analogous result holds for any Eilenberg-Mac Lane space for a finite group. We also compute the Morava $K$-theory of the free loop space of a suspension, and comment on the general problem.References
- Jean-Luc Brylinski, Representations of loop groups, Dirac operators on loop space, and modular forms, Topology 29 (1990), no. 4, 461–480. MR 1071369, DOI 10.1016/0040-9383(90)90016-D
- Edgar H. Brown Jr. and Franklin P. Peterson, A spectrum whose $Z_{p}$ cohomology is the algebra of reduced $p^{th}$ powers, Topology 5 (1966), 149–154. MR 192494, DOI 10.1016/0040-9383(66)90015-2
- G. E. Carlsson and R. L. Cohen, The cyclic groups and the free loop space, Comment. Math. Helv. 62 (1987), no. 3, 423–449. MR 910170, DOI 10.1007/BF02564455
- Ralph L. Cohen, A model for the free loop space of a suspension, Algebraic topology (Seattle, Wash., 1985) Lecture Notes in Math., vol. 1286, Springer, Berlin, 1987, pp. 193–207. MR 922928, DOI 10.1007/BFb0078743
- Tahsin Ghazal, A new example in $K$-theory of loopspaces, Proc. Amer. Math. Soc. 107 (1989), no. 3, 855–856. MR 984790, DOI 10.1090/S0002-9939-1989-0984790-0
- Thomas G. Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985), no. 2, 187–215. MR 793184, DOI 10.1016/0040-9383(85)90055-2
- Michael J. Hopkins, Nicholas J. Kuhn, and Douglas C. Ravenel, Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc. 13 (2000), no. 3, 553–594. MR 1758754, DOI 10.1090/S0894-0347-00-00332-5
- David Copeland Johnson and W. Stephen Wilson, $BP$ operations and Morava’s extraordinary $K$-theories, Math. Z. 144 (1975), no. 1, 55–75. MR 377856, DOI 10.1007/BF01214408
- Haynes Miller, The elliptic character and the Witten genus, Algebraic topology (Evanston, IL, 1988) Contemp. Math., vol. 96, Amer. Math. Soc., Providence, RI, 1989, pp. 281–289. MR 1022688, DOI 10.1090/conm/096/1022688
- Douglas C. Ravenel and W. Stephen Wilson, The Morava $K$-theories of Eilenberg-Mac Lane spaces and the Conner-Floyd conjecture, Amer. J. Math. 102 (1980), no. 4, 691–748. MR 584466, DOI 10.2307/2374093
- Graeme Segal, Elliptic cohomology (after Landweber-Stong, Ochanine, Witten, and others), Astérisque 161-162 (1988), Exp. No. 695, 4, 187–201 (1989). Séminaire Bourbaki, Vol. 1987/88. MR 992209
- N. E. Steenrod, Cohomology operations, Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, N.J., 1962. Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. MR 0145525
- Edward Witten, Elliptic genera and quantum field theory, Comm. Math. Phys. 109 (1987), no. 4, 525–536. MR 885560, DOI 10.1007/BF01208956
- Edward Witten, The index of the Dirac operator in loop space, Elliptic curves and modular forms in algebraic topology (Princeton, NJ, 1986) Lecture Notes in Math., vol. 1326, Springer, Berlin, 1988, pp. 161–181. MR 970288, DOI 10.1007/BFb0078045
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 243-250
- MSC: Primary 55P35; Secondary 19L99, 55N20
- DOI: https://doi.org/10.1090/S0002-9939-1992-1079897-6
- MathSciNet review: 1079897