On Gromov’s conjecture for totally non-spin manifolds
| Autor: | Alexander Dranishnikov, Dmitry Bolotov |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Fundamental group
Conjecture Closed manifold Group (mathematics) Computer Science::Information Retrieval 010102 general mathematics Dimension (graph theory) Astrophysics::Instrumentation and Methods for Astrophysics Duality (optimization) Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 01 natural sciences Combinatorics 0103 physical sciences Computer Science::General Literature 010307 mathematical physics Geometry and Topology 0101 mathematics Abelian group Analysis Mathematics Scalar curvature |
| Zdroj: | Journal of Topology and Analysis. :571-587 |
| ISSN: | 1793-7167 1793-5253 |
| Popis: | Gromov’s conjecture states that for a closed [Formula: see text]-manifold [Formula: see text] with positive scalar curvature, the macroscopic dimension of its universal covering [Formula: see text] satisfies the inequality [Formula: see text] [9]. We prove that for totally non-spin [Formula: see text]-manifolds, the inequality [Formula: see text] implies the inequality [Formula: see text]. This implication together with the main result of [6] allows us to prove Gromov’s conjecture for totally non-spin [Formula: see text]-manifolds whose fundamental group is a virtual duality group with [Formula: see text]. In the case of virtually abelian groups, we reduce Gromov’s conjecture for totally non-spin manifolds to the problem whether [Formula: see text]. This problem can be further reduced to the [Formula: see text]-stability conjecture for manifolds with free abelian fundamental groups. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|