Algebraic & Geometric Topology

On the cohomology equivalences between bundle-type quasitoric manifolds over a cube

Sho Hasui

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

The aim of this article is to establish the notion of bundle-type quasitoric manifolds and provide two classification results on them: (i) (P2 # P2)–bundle type quasitoric manifolds are weakly equivariantly homeomorphic if their cohomology rings are isomorphic, and (ii) quasitoric manifolds over I3 are homeomorphic if their cohomology rings are isomorphic. In the latter case, there are only four quasitoric manifolds up to weakly equivariant homeomorphism which are not bundle-type.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 1 (2017), 25-64.

Dates
Received: 3 December 2014
Revised: 27 February 2016
Accepted: 9 July 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841308

Digital Object Identifier
doi:10.2140/agt.2017.17.25

Mathematical Reviews number (MathSciNet)
MR3604372

Zentralblatt MATH identifier
1357.57057

Subjects
Primary: 57R19: Algebraic topology on manifolds 57S25: Groups acting on specific manifolds

Keywords
quasitoric manifold toric topology

Citation

Hasui, Sho. On the cohomology equivalences between bundle-type quasitoric manifolds over a cube. Algebr. Geom. Topol. 17 (2017), no. 1, 25--64. doi:10.2140/agt.2017.17.25. https://projecteuclid.org/euclid.agt/1510841308


Export citation

References

  • V,M Buchstaber, T,E Panov, Torus actions and their applications in topology and combinatorics, University Lecture Series 24, Amer. Math. Soc., Providence, RI (2002)
  • S Choi, Classification of Bott manifolds up to dimension $8$, Proc. Edinb. Math. Soc. 58 (2015) 653–659
  • S Choi, M Masuda, S Murai, Invariance of Pontrjagin classes for Bott manifolds, Algebr. Geom. Topol. 15 (2015) 965–986
  • S Choi, M Masuda, D,Y Suh, Quasitoric manifolds over a product of simplices, Osaka J. Math. 47 (2010) 109–129
  • S Choi, M Masuda, D,Y Suh, Topological classification of generalized Bott towers, Trans. Amer. Math. Soc. 362 (2010) 1097–1112
  • S Choi, S Park, D,Y Suh, Topological classification of quasitoric manifolds with second Betti number $2$, Pacific J. Math. 256 (2012) 19–49
  • M,W Davis, Smooth $G$–manifolds as collections of fiber bundles, Pacific J. Math. 77 (1978) 315–363
  • M,W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417–451
  • S Hasui, On the classification of quasitoric manifolds over dual cyclic polytopes, Algebr. Geom. Topol. 15 (2015) 1387–1437
  • P,E Jupp, Classification of certain $6$–manifolds, Proc. Cambridge Philos. Soc. 73 (1973) 293–300
  • M Masuda, Equivariant cohomology distinguishes toric manifolds, Adv. Math. 218 (2008) 2005–2012
  • M Masuda, T Panov, On the cohomology of torus manifolds, Osaka J. Math. 43 (2006) 711–746
  • P Orlik, F Raymond, Actions of the torus on $4$–manifolds, I, Trans. Amer. Math. Soc. 152 (1970) 531–559