Algebraic & Geometric Topology

Cohomological non-rigidity of eight-dimensional complex projective towers

Shintarô Kuroki and Dong Youp Suh

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/agt.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

A complex projective tower, or simply P tower, is an iterated complex projective fibration starting from a point. In this paper, we classify a certain class of 8–dimensional P towers up to diffeomorphism. As a consequence, we show that cohomological rigidity is not satisfied by the collection of 8–dimensional P towers: there are two distinct 8–dimensional P towers that have the same cohomology rings.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 2 (2015), 769-782.

Dates
Received: 30 November 2013
Revised: 25 July 2014
Accepted: 12 January 2015
First available in Project Euclid: 28 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895788

Digital Object Identifier
doi:10.2140/agt.2015.15.769

Mathematical Reviews number (MathSciNet)
MR3342675

Zentralblatt MATH identifier
1320.57033

Subjects
Primary: 57R22: Topology of vector bundles and fiber bundles [See also 55Rxx]
Secondary: 57S25: Groups acting on specific manifolds

Keywords
complex projective bundles cohomological rigidity problem toric topology

Citation

Kuroki, Shintarô; Suh, Dong Youp. Cohomological non-rigidity of eight-dimensional complex projective towers. Algebr. Geom. Topol. 15 (2015), no. 2, 769--782. doi:10.2140/agt.2015.15.769. https://projecteuclid.org/euclid.agt/1511895788


Export citation

References

  • M,F Atiyah, E Rees, Vector bundles on projective $3$–space, Invent. Math. 35 (1976) 131–153
  • A Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. 57 (1953) 115–207
  • V,M Buchstaber, T,E Panov, Torus actions and their applications in topology and combinatorics, University Lecture Series 24, Amer. Math. Soc. (2002)
  • S Choi, M Masuda, D,Y Suh, Topological classification of generalized Bott towers, Trans. Amer. Math. Soc. 362 (2010) 1097–1112
  • S Choi, M Masuda, D,Y Suh, Rigidity problems in toric topology: A survey, Tr. Mat. Inst. Steklova 275 (2011) 188–201
  • Y Fukukawa, H Ishida, M Masuda, The cohomology ring of the GKM graph of a flag manifold of classical type, Kyoto J. Math. 54 (2014) 653–677
  • S Kuroki, D,Y Suh, Complex projective towers and their cohomological rigidity up to dimension six to appear in Proc. Steklov Inst. Math.
  • M Mimura, H Toda, Homotopy groups of ${\rm SU}(3)$, ${\rm SU}(4)$ and ${\rm Sp}(2)$, J. Math. Kyoto Univ. 3 (1963) 217–250