The transfer and symplectic cobordism

Author:
Malkhaz Bakuradze

Journal:
Trans. Amer. Math. Soc. **349** (1997), 4385-4399

MSC (1991):
Primary 55N22, 55R12

DOI:
https://doi.org/10.1090/S0002-9947-97-01867-9

MathSciNet review:
1407478

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Abstract | References | Similar Articles | Additional Information

Abstract: The main result of this paper is the nilpotency fomula , for N. Ray classes in the torsion of the symplectic bordism ring

**[BaNa]**M. Bakuradze and R. Nadiradze,*Cohomological realizations of two-valued formal groups and their application.*, Proc. Tbilisi A. Razmadze Math. Inst.**94**(1991), 12-28 (Russian) MR**94d:55011**.**[BG]**J.C. Becker and D.H. Gottlieb,*The transfer map and fibre bundles*, Topology**14**(1975), 1-12. MR**51:14042****[BM]**G. Brumfiel and I. Madsen,*Evalution of the transfer and the universal surgery classes*, Inventiones Math**32**(1976), 133-169. MR**54:1220****[BO]**J.M. Boardman,*Stable homotopy theory*, mimeographed notes, University of Warwick (1966).**[Bu]**V.M. Buchstaber,*Characteristic classes in cobordisms and topological applications of theories of one and two-valued formal groups*, Itogi Nauki i Tekniki**10**(1977), 5-178; English transl. in J. Soviet Math.**11**(1979), no. 6. MR**80g:55008****[D]**A. Dold,*The fixed point transfer of fibre preserving maps*, Math. Z**148**(1976), 215-244. MR**55:6416****[Fe]**M. Feshbach,*The transfer and compact Lie groups*, Trans. Amer. Math. Soc.**251**(1979, July), 139-169. MR**80k:55049****[G]**V.G. Gorbunov,*Symplectic cobordism of projective spaces*, Mat. Sbornik**181**(1990), 506-520; English transl. in Math. USSR Sb.**69**(1991). MR**91i:55006****[GR]**V.G. Gorbunov and N. Ray,*Orientation of bundles and symplectic cobordism*, Publ. RIMS Kyoto Univ.**28, 1**(1992), 39-55. MR**93e:55008****[Mo]**K. Morisugi,*Massey products in and its application*, J. Math. Kyoto Univ.**23, 2**(1983), 239-269. MR**85g:55009****[Na]**R. Nadiradze,*Characteristic classes in the theory and their applications*I, Baku Intern. Top. Conf. Abstracts (1987), 213; II, Preprint, Tbilisi, Razmadze Math. Inst. (1991), 1-11; III Preprint, vol. 58, Heidelberg, 1993, pp. 1-21.**[R]**N. Ray,*Indecomposables in*, Topology**10**(1971), 261-270. MR**45:9342****[RS]**N. Ray and R. Switzer,*The algebraic topology of Landweber's and Alexander's manifolds*, Mem. Amer. Math. Soc.**193**(1977), Chapter II, pp. 28-42. MR**57:1505****[Ro]**F.W. Roush,*On some torsion classes in symplectic bordism*, unpublished.**[Sn]**V.P. Snaith,*Algebraic cobordism and theory*, Mem. Amer. Math. Soc.**21**(1979), no. 221. MR**80k:57060****[V]**V.V. Vershinin,*Computation of the symplectic cobordism ring in dimensions less than 32 and the non-triviality of the majority of the triple products of Ray's elements*, Sibirsk. Mat. Zh.**24**(1983), 50-63; English transl. in Siberian Math. J.**24**(1983). MR**84f:57020**

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Additional Information

**Malkhaz Bakuradze**

Affiliation:
A. Razmadze Mathematics Institute of the Georgian Academy of Sciences, M. Aleksidze st. 1, 380093, Tbilisi, Republic of Georgia

Email:
maxo@imath.acnet.ge

DOI:
https://doi.org/10.1090/S0002-9947-97-01867-9

Keywords:
Symplectic cobordism,
Euler class,
classifying space,
transfer

Received by editor(s):
July 31, 1995

Additional Notes:
The research described in this publication was made possible in part by Grant RVJ 000 from the International Science Foundation.

Article copyright:
© Copyright 1997
American Mathematical Society