Estimates of Covering Type and the Number of Vertices of Minimal Triangulations
| Autor: | Dejan Govc, Wacław Marzantowicz, Petar Pavešić |
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| Rok vydání: | 2019 |
| Předmět: |
050101 languages & linguistics
Homotopy 05 social sciences Multiplicative function 02 engineering and technology Mathematics::Algebraic Topology Cohomology ring Theoretical Computer Science Combinatorics Computational Theory and Mathematics Mathematics::K-Theory and Homology Mathematics::Category Theory 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Lusternik–Schnirelmann category 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences Geometry and Topology Invariant (mathematics) Mathematics Singular homology |
| Zdroj: | Discrete & Computational Geometry. 63:31-48 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-019-00092-z |
| Popis: | The covering type of a space $X$ is a numerical homotopy invariant which in some sense measures the homotopical size of $X$. It was first introduced by Karoubi and Weibel (in Enseign Math 62(3-4):457-474, 2016) as the minimal cardinality of a good cover of a space $Y$ taken among all spaces that are homotopy equivalent to $X$. We give several estimates of the covering type in terms of other homotopy invariants of $X$, most notably the ranks of the homology groups of $X$, the multiplicative structure of the cohomology ring of $X$ and the Lusternik-Schnirelmann category of $X$. In addition, we relate the covering type of a triangulable space to the number of vertices in its minimal triangulations. In this way we derive within a unified framework several estimates of vertex-minimal triangulations which are either new or extensions of results that have been previously obtained by ad hoc combinatorial arguments. |
| Databáze: | OpenAIRE |
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