Tor decomposition of bup* (BZ/p)^n

  • Khairia Mohamed Mira Department of Mathematics, Faculty of Science, Tripoli University, Libya
Keywords: The connective unitary K-theory,a kunneth formula short exact sequence.

Abstract

We decompose bup* (BZ/p)^n, the connective unitary K- theory with p-adic coefficients of the n-fold smash product of the classifying space for the cyclic group of prime order p, as a direct sum of some graded groups, which include the graded groups bup* (BZ/p) and Tor^1_{\Z_p[v]}(bu_{p^*}(B\Z/p), bu_{p^*}(B\Z/p))[-1]. We deal with the results in [Theorem 3.8]{MK17} together with the Kunneth sequence for bu_{p^*}(B\Z/p)^n, to explain that there is no extension problem for this Kunneth sequence, for any finite number n not just for n=2 and therefore the middle term of this sequence is a direct sum of the left and the right side.

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References

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[6] Mira, Khairia M: bu∗(BZ/p) n as a Graded Group; Journal of Progressive Research in Mathematics(JJRM)
ISSN: 2395-0218, SCITECH RESEARCH ORGANISATION, , 1981-1988, Volume 12, Issue 3 available at
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[7] Bruner, Robert R. and Mira, Khairia M. and Stanley, Laura A. and Snaith, Victor P: Ossa’s theorem
via the K¨unneth formula; Mathematics and Statistics 3(3): 58-64, 2015, DOI: 10.13189/ms.2015.030302,
http://www.hrpub.org/download/20150620/MS2-13403792.pdf
Published
2018-03-06
How to Cite
Mira, K. (2018). Tor decomposition of bup* (BZ/p)^n. Journal of Progressive Research in Mathematics, 13(2), 2220-2232. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1427
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Articles