Algebraic & Geometric Topology

Norm minima in certain Siegel leaves

Li Cai

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

In this paper we shall illustrate that each polytopal moment-angle complex can be understood as the intersection of the minima of corresponding Siegel leaves and the unit sphere, with respect to the maximum norm. Consequently, an alternative proof of a rigidity theorem of Bosio and Meersseman is obtained; as piecewise linear manifolds, polytopal real moment-angle complexes can be smoothed in a natural way.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 445-466.

Dates
Received: 11 April 2014
Revised: 3 July 2014
Accepted: 21 July 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510840919

Digital Object Identifier
doi:10.2140/agt.2015.15.445

Mathematical Reviews number (MathSciNet)
MR3325744

Zentralblatt MATH identifier
1330.57042

Subjects
Primary: 57R30: Foliations; geometric theory
Secondary: 57R70: Critical points and critical submanifolds 05E45: Combinatorial aspects of simplicial complexes

Keywords
foliation moment-angle manifold simplicial complex

Citation

Cai, Li. Norm minima in certain Siegel leaves. Algebr. Geom. Topol. 15 (2015), no. 1, 445--466. doi:10.2140/agt.2015.15.445. https://projecteuclid.org/euclid.agt/1510840919


Export citation

References

  • A Bahri, M Bendersky, F,R Cohen, S Gitler, The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces, Adv. Math. 225 (2010) 1634–1668
  • I,V Baskakov, Triple Massey products in the cohomology of moment-angle complexes, Uspekhi Mat. Nauk 58 (2003) 199–200
  • F Bosio, L Meersseman, Real quadrics in $\mathbb{C}\sp n$, complex manifolds and convex polytopes, Acta Math. 197 (2006) 53–127
  • V,M Buchstaber, T,E Panov, Toric topology
  • V,M Buchstaber, T,E Panov, Torus actions and their applications in topology and combinatorics, Univ. Lecture Series 24, Amer. Math. Soc. (2002)
  • C Camacho, N,H Kuiper, J Palis, The topology of holomorphic flows with singularity, Inst. Hautes Études Sci. Publ. Math. (1978) 5–38
  • M,W Davis, When are two Coxeter orbifolds diffeomorphic?, Michigan Math. J. 63 (2014) 401–421
  • M,W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417–451
  • G Denham, A,I Suciu, Moment-angle complexes, monomial ideals and Massey products, Pure Appl. Math. Q. 3 (2007) 25–60
  • S Gitler, S López de Medrano, Intersections of quadrics, moment-angle manifolds and connected sums, Geom. Topol. 17 (2013) 1497–1534
  • M Goresky, R MacPherson, Stratified Morse theory, Ergeb. Math. Grenzgeb. 14, Springer, Berlin (1988)
  • B Grünbaum, Convex polytopes, 2nd edition, Graduate Texts in Math. 221, Springer, New York (2003)
  • S López de Medrano, Topology of the intersection of quadrics in $\mathbb{R}\sp n$, from: “Algebraic topology”, (G Carlsson, R,L Cohen, H,R Miller, D,C Ravenel, editors), Lecture Notes in Math. 1370, Springer, New York (1989) 280–292
  • S López de Medrano, A Verjovsky, A new family of complex, compact, nonsymplectic manifolds, Bol. Soc. Brasil. Mat. 28 (1997) 253–269
  • L Meersseman, A new geometric construction of compact complex manifolds in any dimension, Math. Ann. 317 (2000) 79–115
  • L Meersseman, A Verjovsky, Holomorphic principal bundles over projective toric varieties, J. Reine Angew. Math. 572 (2004) 57–96
  • T,E Panov, Geometric structures on moment-angle manifolds, Uspekhi Mat. Nauk 68 (2013) 111–186 In Russian; translated in Russian Math. Surveys 68 (2013) 503–568
  • T,E Panov, Y Ustinovsky, Complex-analytic structures on moment-angle manifolds, Mosc. Math. J. 12 (2012) 149–172
  • C,P Rourke, B,J Sanderson, Ergeb. Math. Grenzgeb. 69, Springer, New York (1972)
  • J,H,C Whitehead, On $C\sp 1$–complexes, Ann. of Math. 41 (1940) 809–824
  • M Wiemeler, Exotic torus manifolds and equivariant smooth structures on quasitoric manifolds, Math. Z. 273 (2013) 1063–1084