Transfers of Chern classes in BP-cohomology and Chow rings
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- by Björn Schuster and Nobuaki Yagita
- Trans. Amer. Math. Soc. 353 (2001), 1039-1054
- DOI: https://doi.org/10.1090/S0002-9947-00-02647-7
- Published electronically: August 8, 2000
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Abstract:
The $BP^*$-module structure of $BP^*(BG)$ for extraspecial $2$-groups is studied using transfer and Chern classes. These give rise to $p$-torsion elements in the kernel of the cycle map from the Chow ring to ordinary cohomology first obtained by Totaro.References
- J. F. Adams, Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996. With a foreword by J. Peter May; Edited by Zafer Mahmud and Mamoru Mimura. MR 1428422
- Erich Rothe, Topological proofs of uniqueness theorems in the theory of differential and integral equations, Bull. Amer. Math. Soc. 45 (1939), 606–613. MR 93, DOI 10.1090/S0002-9904-1939-07048-1
- K. Geetha, The semigroup of singular endomorphisms, Semigroup Forum 58 (1999), no. 2, 207–221. MR 1658646, DOI 10.1007/s002339900015
- David John Green and Pham Anh Minh, Transfer and Chern classes for extraspecial $p$-groups, Group representations: cohomology, group actions and topology (Seattle, WA, 1996) Proc. Sympos. Pure Math., vol. 63, Amer. Math. Soc., Providence, RI, 1998, pp. 245–255. MR 1603167, DOI 10.1090/pspum/063/1603167
- Masana Harada and Akira Kono, On the integral cohomology of extraspecial $2$-groups, Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985), 1987, pp. 215–219. MR 885105, DOI 10.1016/0022-4049(87)90025-9
- Michael J. Hopkins, Nicholas J. Kuhn, and Douglas C. Ravenel, Morava $K$-theories of classifying spaces and generalized characters for finite groups, Algebraic topology (San Feliu de Guíxols, 1990) Lecture Notes in Math., vol. 1509, Springer, Berlin, 1992, pp. 186–209. MR 1185970, DOI 10.1007/BFb0087510
- Akira Kono and Nobuaki Yagita, Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups, Trans. Amer. Math. Soc. 339 (1993), no. 2, 781–798. MR 1139493, DOI 10.1090/S0002-9947-1993-1139493-4
- Igor Kriz, Morava $K$-theory of classifying spaces: some calculations, Topology 36 (1997), no. 6, 1247–1273. MR 1452850, DOI 10.1016/S0040-9383(96)00049-3
- Daniel Quillen, The $\textrm {mod}$ $2$ cohomology rings of extra-special $2$-groups and the spinor groups, Math. Ann. 194 (1971), 197–212. MR 290401, DOI 10.1007/BF01350050
- D. C. Ravenel, W. S. Wilson and N. Yagita. Brown-Peterson cohomology from Morava $K$-theory. $K$-Theory 15 (1998), 147–199.
- Björn Schuster, On the Morava $K$-theory of some finite $2$-groups, Math. Proc. Cambridge Philos. Soc. 121 (1997), no. 1, 7–13. MR 1418356, DOI 10.1017/S0305004196001156
- Burt Totaro, Torsion algebraic cycles and complex cobordism, J. Amer. Math. Soc. 10 (1997), no. 2, 467–493. MR 1423033, DOI 10.1090/S0894-0347-97-00232-4
- B. Totaro. The Chow ring of classifying spaces. To appear.
- Nobuaki Yagita, Cohomology for groups of $\textrm {rank}_pG=2$ and Brown-Peterson cohomology, J. Math. Soc. Japan 45 (1993), no. 4, 627–644. MR 1239340, DOI 10.2969/jmsj/04540627
- Nobuaki Yagita, On relations between Brown-Peterson cohomology and the ordinary mod $p$ cohomology theory, Kodai Math. J. 7 (1984), no. 2, 273–285. MR 744140, DOI 10.2996/kmj/1138036912
Bibliographic Information
- Björn Schuster
- Affiliation: FB 7 Mathematik, Bergische Universität-Gesamthochschule Wuppertal, 42097 Wuppertal, Germany
- Email: schuster@math.uni-wuppertal.de
- Nobuaki Yagita
- Affiliation: Department of Mathematics, Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan
- MR Author ID: 185110
- Email: yagita@mito.ipc.ibaraki.ac.jp
- Received by editor(s): March 29, 1999
- Published electronically: August 8, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 1039-1054
- MSC (2000): Primary 55P35, 57T25; Secondary 55R35, 57T05
- DOI: https://doi.org/10.1090/S0002-9947-00-02647-7
- MathSciNet review: 1804412