Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T20:58:45.183Z Has data issue: false hasContentIssue false
  • English
  • Français

ENDOMORPHISMS OF EXOTIC MODELS

Published online by Cambridge University Press:  20 June 2018

EUGENIA ELLIS ,
CONSTANZE ROITZHEIM ,
LAURA SCULL  and
CAROLYN YARNALL
EUGENIA ELLIS
Affiliation:
Universidad de la República, IMERL, Facultad de Ingenierí a, Julio Herrera y Reissig 565, Montevideo CP 11300, Uruguay e-mail: [email protected]
CONSTANZE ROITZHEIM
Affiliation:
University of Kent, School of Mathematics, Statistics and Actuarial Science, Sibson, Canterbury CT2 7FS, United Kingdom e-mail: [email protected]
LAURA SCULL
Affiliation:
Department of Mathematics, Fort Lewis College, 1000 Rim Drive, Durango, CO 81301, USA e-mail: [email protected]
CAROLYN YARNALL
Affiliation:
University of Kentucky, Department of Mathematics, 767 Patterson Office Tower, Lexington, KY 40506, USA e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We calculate the endomorphism dga of Franke's exotic algebraic model for the K-local stable homotopy category at odd primes. We unravel its original abstract structure to give explicit generators, differentials and products.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 2 , May 2019 , pp. 321 - 348
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

REFERENCES

1. Adams, J. F. and Clarke, F. W., Stable operations on complex K-theory, Ill. J. Math. 21 (1977), 826–829.Google Scholar
2. Adams, J. F., Harris, A. S. and Switzer, R. M., Hopf algebras of cooperations for real and complex K-theory, Proc. Lond. Math. Soc., s3-23 (1971), 385–408.Google Scholar
3. Barnes, D. and Roitzheim, C., Local framings, N. Y. J. Math. 17 (2011), 513–552.Google Scholar
4. Bousfield, A. K., The localization of spectra with respect to homology, Topology 18 (1979), 257–281.Google Scholar
5. Bousfield, A. K., On the homotopy theory of K-local spectra at an odd prime, Am. J. Math. 107 (1985), 895–932.Google Scholar
6. Clarke, F., Crossley, M. and Whitehouse, S., Algebras of operations in K-theory, Topology 44 (2005), 151–174.Google Scholar
7. Dugger, D., Spectral enrichments of model categories, Homol., Homotopy Appl. 8 (2006), 1–30.Google Scholar
8. Dugger, D., Replacing model categories with simplicial ones. Trans. Am. Math. Soc. 12 (2001), 5003–5027.Google Scholar
9. Dugger, D. and Shipley, B., Topological equivalences for differential graded algebras, Adv. Math. 212 (2007), 37–61.Google Scholar
10. Franke, J., Uniqueness theorems for certain triangulated categories possessing an Adams spectral sequence (1996). Available at http://www.math.uiuc.edu/K-theory/0139/.Google Scholar
11. Hovey, M., Homotopy theory of comodules over a Hopf algebroid, Contemp. Math. 346 (2004), 261–304.Google Scholar
12. Johnson, K., The algebra of stable operations for complex p-local K-theory, Can. Math. Bull. 30 (1987), 57–62.Google Scholar
13. Patchkoria, I., On the algebraic classification of module spectra, Algebraic Geom. Topol. 12 (2012), 2329–2388.Google Scholar
14. Patchkoria, I., On exotic equivalences and a theorem of Franke. Available at https://arxiv.org/pdf/1612.03732.pdf.Google Scholar
15. Ravenel, D. C.. Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics, vol. 121 (Academic Press Inc., Orlando, FL, 1986).Google Scholar
16. Roitzheim, C., Rigidity and exotic models for the K-local stable homotopy category. Geom. Topol. 11 (2007), 1855–1886.Google Scholar
17. Roitzheim, C., On the algebraic classification of K-local spectra, Homology, Homotopy Appl., 10 (2008), 389–412.Google Scholar
18. Roitzheim, C., A case of monoidal uniqueness of algebraic models, Forum Math. 27 (6) (2015), 3615–3634.Google Scholar
19. Schwede, S., The stable homotopy category is rigid, Ann. Math. (2), 166 (2007), 837–863.Google Scholar
20. Schwede, S. and Shipley, B., Stable model categories are categories of modules. Topology 42 (2003), 103–153.Google Scholar
21. Strong, M. J. and Whitehouse, S., Infinite sums of unstable Adams operations and cobordism, J. Pure Appl. Algebra 214 (2010), 910–918.Google Scholar