Hurewicz fibrations, almost submetries and critical points of smooth maps
-
Sergio Luigi Cacciatori
and
Stefano Pigola
Abstract
We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric properties of maps between compact Riemannian manifolds under curvature restrictions.
References
[1] M. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren Math. Wiss. 319, Springer, Berlin, 1999. 10.1007/978-3-662-12494-9Search in Google Scholar
[2] R. Engelking, Dimension Theory, North-Holland Math. Lib. 19, North-Holland, Amsterdam, 1978. Search in Google Scholar
[3] R. Fritsch and R. Piccinini, Cellular Structures in Topology, Cambridge Stud. Adv. Math, Cambridge University Press, Cambridge, 1990. 10.1017/CBO9780511983948Search in Google Scholar
[4] R. Godement, Topologie Algebrique et Theorie des Faisceaux, Hermann, Paris, 1973. Search in Google Scholar
[5] D. H. Gottlieb, Robots and fibre bundles, Bull. Soc. Math. Belg. Sér. A 38 (1986), 219–223. Search in Google Scholar
[6] A. Hatcher, Algebraic Topology, Cambridge University Press, Cambridge, 2002. Search in Google Scholar
[7] J. M. Lee, Introduction to topological manifolds, Grad. Texts in Math. 202, Springer, New York, 2011. 10.1007/978-1-4419-7940-7Search in Google Scholar
[8] J. Milnor, On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959), 272–280. 10.2307/1993204Search in Google Scholar
[9] H. Miyazaki, The paracompactness of CW-complexes, Tohoku Math. J. (2) 4 (1952), 309–313. 10.2748/tmj/1178245380Search in Google Scholar
[10] J. Munkres, Elements of Algebraic Topology, Perseus Books Group, New York, 1984. Search in Google Scholar
[11]
X. Rong and S. Xu,
Stability of
[12] J. P. Serre, Homologie singulière des espaces fibrés, Ann. of Math. (2) 54 (1951), 425–505. 10.2307/1969485Search in Google Scholar
[13] E. H. Spanier, Algebraic Topology, Springer, New York, 1981. 10.1007/978-1-4684-9322-1Search in Google Scholar
[14] F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Grad. Texts in Math. 94, Springer, New York, 1983. 10.1007/978-1-4757-1799-0Search in Google Scholar
[15]
S. Xu,
Homotopy lifting property of an
[16] T. Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. (2) 133 (1991), no. 2, 317–357. 10.2307/2944340Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Hurewicz fibrations, almost submetries and critical points of smooth maps
- Lower bounds for regular genus and gem-complexity of PL 4-manifolds
- Diffusion semigroup on manifolds with time-dependent metrics
- Blow-up algebras, determinantal ideals, and Dedekind–Mertens-like formulas
- A computational approach to Milnor fiber cohomology
- Metrical universality for groups
- The second and third moment of L(1/2,χ) in the hyperelliptic ensemble
- Slender domains and compact domains
- Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs
- A note on local Hardy spaces
- On the value group of a model of Peano Arithmetic
- Extremal values of the (fractional) Weinstein functional on the hyperbolic space
- Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
- Unitals in shift planes of odd order
Articles in the same Issue
- Frontmatter
- Hurewicz fibrations, almost submetries and critical points of smooth maps
- Lower bounds for regular genus and gem-complexity of PL 4-manifolds
- Diffusion semigroup on manifolds with time-dependent metrics
- Blow-up algebras, determinantal ideals, and Dedekind–Mertens-like formulas
- A computational approach to Milnor fiber cohomology
- Metrical universality for groups
- The second and third moment of L(1/2,χ) in the hyperelliptic ensemble
- Slender domains and compact domains
- Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs
- A note on local Hardy spaces
- On the value group of a model of Peano Arithmetic
- Extremal values of the (fractional) Weinstein functional on the hyperbolic space
- Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
- Unitals in shift planes of odd order
