The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3

Yoshitaka Nakazawa; Katsumi Shimomura

Fundamenta Mathematicae (1997)

  • Volume: 152, Issue: 1, page 1-20
  • ISSN: 0016-2736

Abstract

top
For the Brown-Peterson spectrum BP at the prime 3, v 2 denotes Hazewinkel’s second polynomial generator of B P * . Let L 2 denote the Bousfield localization functor with respect to v 2 - 1 B P . A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups π * ( L 2 M ∧ X ) for the 8 skeleton X of BP.

How to cite

top

Nakazawa, Yoshitaka, and Shimomura, Katsumi. "The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3." Fundamenta Mathematicae 152.1 (1997): 1-20. <http://eudml.org/doc/212196>.

@article{Nakazawa1997,
abstract = {For the Brown-Peterson spectrum BP at the prime 3, $v_2$ denotes Hazewinkel’s second polynomial generator of $BP_*$. Let $L_2$ denote the Bousfield localization functor with respect to $v_2^\{-1\}BP$. A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups $π_*(L_2M ∧ X)$ for the 8 skeleton X of BP.},
author = {Nakazawa, Yoshitaka, Shimomura, Katsumi},
journal = {Fundamenta Mathematicae},
keywords = {homotopy groups; Adams-Novikov spectral sequence; Johnson-Wilson spectrum; coalgebroid; duality; iterated Adams map},
language = {eng},
number = {1},
pages = {1-20},
title = {The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3},
url = {http://eudml.org/doc/212196},
volume = {152},
year = {1997},
}

TY - JOUR
AU - Nakazawa, Yoshitaka
AU - Shimomura, Katsumi
TI - The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3
JO - Fundamenta Mathematicae
PY - 1997
VL - 152
IS - 1
SP - 1
EP - 20
AB - For the Brown-Peterson spectrum BP at the prime 3, $v_2$ denotes Hazewinkel’s second polynomial generator of $BP_*$. Let $L_2$ denote the Bousfield localization functor with respect to $v_2^{-1}BP$. A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups $π_*(L_2M ∧ X)$ for the 8 skeleton X of BP.
LA - eng
KW - homotopy groups; Adams-Novikov spectral sequence; Johnson-Wilson spectrum; coalgebroid; duality; iterated Adams map
UR - http://eudml.org/doc/212196
ER -

References

top
  1. [1] Y. Arita and K. Shimomura, The chromatic E 1 -term H 1 M 1 1 at the prime 3, Hiroshima Math. J. 26 (1996), 415-431. Zbl0869.55010
  2. [2] M. J. Hopkins and B. H. Gross, The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory, Bull. Amer. Math. Soc. 30 (1994), 76-86. Zbl0857.55003
  3. [3] M. Mahowald and K. Shimomura, The Adams-Novikov spectral sequence for the L 2 -localization of a v 2 -spectrum, in: Contemp. Math. 146, Amer. Math. Soc., 1993, 237-250. Zbl0791.55005
  4. [4] H. R. Miller, D. C. Ravenel, and W. S. Wilson, Periodic phenomena in Adams-Novikov spectral sequence, Ann. of Math. 106 (1977), 469-516. Zbl0374.55022
  5. [5] D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, 1986. 
  6. [6] D. C. Ravenel, Nilpotence and Periodicity in Stable Homotopy Theory, Ann. of Math. Stud. 128, Princeton Univ. Press, 1992. 
  7. [7] K. Shimomura, On the Adams-Novikov spectral sequence and products of β-elements, Hiroshima Math. J. 16 (1986), 209-224. Zbl0605.55013
  8. [8] K. Shimomura, The homotopy groups of the L 2 -localized Mahowald spectrum X⟨1⟩, Forum Math. 7 (1995), 685-707. Zbl0835.55009
  9. [9] K. Shimomura, The homotopy groups of the L 2 -localized Toda-Smith spectrum V(1) at the prime 3, Trans. Amer. Math. Soc., to appear. Zbl0869.55012
  10. [10] K. Shimomura and H. Tamura, Non-triviality of some compositions of β-elements in the stable homotopy of Moore spaces, Hiroshima Math. J. 16 (1986), 121-133. Zbl0606.55009
  11. [11] K. Shimomura and A. Yabe, The homotopy groups π * ( L 2 S 0 ) , Topology 34 (1995), 261-289. Zbl0832.55011

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.