Abstract
We find conditions which ensure that the topological complexity of a closed manifold M with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes
results of Costa and Farber on the topological complexity of spaces with small fundamental group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik–Schnirelmann category of the cofibre of the diagonal map
Funding source: Fundação para a Ciência e a Tecnologia
Award Identifier / Grant number: UIDB/00013/2020
Award Identifier / Grant number: UIDP/00013/2020
Funding statement: The second author is partially supported by Portuguese Funds through FCT – Fundação para a Ciência e a Tecnologia – within the projects UIDB/00013/2020 and UIDP/00013/2020.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the topological complexity of manifolds with abelian fundamental group
- Reconstructing étale groupoids from semigroups
- Fiberwise linear differential operators
- Foliations with isolated singularities on Hirzebruch surfaces
- On a stronger reconstruction notion for monoids and clones
- Cochain level May–Steenrod operations
- Commutative L-algebras and measure theory
- Rankin–Selberg integrals for principal series representations of GL(n)
- A simple proof of the generalized Leibniz rule on bounded Euclidean domains
- Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras
- Seshadri constants on some Quot schemes
- Hörmander Fourier multiplier theorems with optimal Besov regularity on multi-parameter Hardy spaces
- On spectral and non-spectral problem for the planar self-similar measures with four element digit sets
- C-minimal topological groups
- Cevian properties in ideal lattices of Abelian ℓ-groups
- Study of twisted Bargmann transform via Bargmann transform
Articles in the same Issue
- Frontmatter
- On the topological complexity of manifolds with abelian fundamental group
- Reconstructing étale groupoids from semigroups
- Fiberwise linear differential operators
- Foliations with isolated singularities on Hirzebruch surfaces
- On a stronger reconstruction notion for monoids and clones
- Cochain level May–Steenrod operations
- Commutative L-algebras and measure theory
- Rankin–Selberg integrals for principal series representations of GL(n)
- A simple proof of the generalized Leibniz rule on bounded Euclidean domains
- Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras
- Seshadri constants on some Quot schemes
- Hörmander Fourier multiplier theorems with optimal Besov regularity on multi-parameter Hardy spaces
- On spectral and non-spectral problem for the planar self-similar measures with four element digit sets
- C-minimal topological groups
- Cevian properties in ideal lattices of Abelian ℓ-groups
- Study of twisted Bargmann transform via Bargmann transform