A note on the Hilali conjecture
-
Manuel Amann
Abstract
In this short note we observe that the Hilali conjecture holds for 2-stage spaces, i.e. we argue that the dimension of the rational cohomology is at least as large as the dimension of the rational homotopy groups for these spaces. We also prove the Hilali conjecture for a class of spaces which puts it into the context of fibrations.
References
[1] Félix Y., Halperin S. and Thomas J.-C., Rational Homotopy Theory, Grad. Texts in Math. 205, Springer, New York, 2001. 10.1007/978-1-4613-0105-9Suche in Google Scholar
[2] Félix Y., Oprea J. and Tanré D., Algebraic Models in Geometry, Oxf. Grad. Texts Math. 17, Oxford University Press, Oxford, 2008. 10.1093/oso/9780199206513.001.0001Suche in Google Scholar
[3] Fernández de Bobilla J., Fresán J., Munõz V. and Murillo A., The Hilali conjecture for hyperelliptic spaces, Mathematics Without Boundaries, Springer, New York (2014), 21–36. 10.1007/978-1-4939-1106-6_2Suche in Google Scholar
[4]
Hilali M. R.,
Action du tore
[5] Hilali M. R. and Mamouni M. I., A conjectured lower bound for the cohomological dimension of elliptic spaces, J. Homotopy Relat. Struct. 3 (2008), no. 1, 379–384. Suche in Google Scholar
[6] Hilali M. R. and Mamouni M. I., A lower bound of cohomologic dimension for an elliptic space, Topology Appl. 156 (2008), no. 2, 274–283. 10.1016/j.topol.2008.07.011Suche in Google Scholar
[7] Hilali M. R. and Mamouni M. I., A conjectured lower bound for the cohomological dimension of elliptic spaces – Recent results in some simple cases, preprint 2013, http://arxiv.org/abs/0803.3821. Suche in Google Scholar
[8] Hilali M. R. and Mamouni M. I., La conjecture H: Une minoration de la dimension cohomologique pour un espace elliptique, preprint 2013, https://arxiv.org/abs/0712.3784. Suche in Google Scholar
[9] Jessup B. and Lupton G., Free torus actions and two-stage spaces, Math. Proc. Cambridge Philos. Soc. 137 (2004), no. 1, 191–207. 10.1017/S0305004103007242Suche in Google Scholar
[10] Nakamura O. and Yamaguchi T., Lower bounds of Betti numbers of elliptic spaces with certain formal dimensions, Kochi J. Math. 6 (2001), 9–28. Suche in Google Scholar
© 2017 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- A note on the Hilali conjecture
- Finite groups have more conjugacy classes
- The gauge action, DG Lie algebras and identities for Bernoulli numbers
- Unitary embeddings of finite loop spaces
- Topological complexity of planar polygon spaces with small genetic code
- Numerical semigroups in a problem about cost-effective transport
- On the smallest simultaneous power nonresidue modulo a prime
- Decompositions of the higher order polars of plane branches
- A formula for the expected volume of the Wiener sausage with constant drift
-
The slice spectral sequence for the
- Incidences between points and generalized spheres over finite fields and related problems
- Mean values of the Witten L-function for SU(2)
- A direct computation of the cohomology of the braces operad
- Abelian varieties over finite fields as basic abelian varieties
Artikel in diesem Heft
- Frontmatter
- A note on the Hilali conjecture
- Finite groups have more conjugacy classes
- The gauge action, DG Lie algebras and identities for Bernoulli numbers
- Unitary embeddings of finite loop spaces
- Topological complexity of planar polygon spaces with small genetic code
- Numerical semigroups in a problem about cost-effective transport
- On the smallest simultaneous power nonresidue modulo a prime
- Decompositions of the higher order polars of plane branches
- A formula for the expected volume of the Wiener sausage with constant drift
-
The slice spectral sequence for the
- Incidences between points and generalized spheres over finite fields and related problems
- Mean values of the Witten L-function for SU(2)
- A direct computation of the cohomology of the braces operad
- Abelian varieties over finite fields as basic abelian varieties
