Cohomological uniqueness, Massey products and the modular isomorphism problem for $2$-groups of maximal nilpotency class
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- by Albert Ruiz and Antonio Viruel PDF
- Trans. Amer. Math. Soc. 365 (2013), 3729-3751 Request permission
Abstract:
Let $G$ be a finite $2$-group of maximal nilpotency class, and let $BG$ be its classifying space. We prove that iterated Massey products in $H^*(BG;\mathbb {F}_2)$ do characterize the homotopy type of $BG$ among $2$-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for $2$-groups of maximal nilpotency class.References
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Additional Information
- Albert Ruiz
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Spain
- Email: Albert.Ruiz@uab.cat
- Antonio Viruel
- Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Apdo correos 59, 29080 Málaga, Spain
- MR Author ID: 630145
- ORCID: 0000-0002-1605-5845
- Email: viruel@agt.cie.uma.es
- Received by editor(s): April 29, 2011
- Received by editor(s) in revised form: November 3, 2011
- Published electronically: January 24, 2013
- Additional Notes: The first author was partially supported by FEDER-MEC grant MTM2010-20692
The second author was partially supported by FEDER-MEC grant MTM2010-18089 and Junta de Andalucía grants FQM-213 and P07-FQM-2863
Both authors were partially supported by Generalitat de Catalunya grant 2009SGR-1092. - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 3729-3751
- MSC (2010): Primary 55R35, 20D15
- DOI: https://doi.org/10.1090/S0002-9947-2013-05756-X
- MathSciNet review: 3042601