Approximation of metric spaces by Reeb graphs: Cycle rank of a Reeb graph, the co-rank of the fundamental group, and large components of level sets on Riemannian manifolds

DOI10.2298/FIL1907031GWikidataQ115229895 ScholiaQ115229895MaRDI QIDQ5080823

Irina Gelbukha

Publication date: 31 May 2022

Published in: Filomat (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.00777

zbMATH Keywords

Riemannian manifoldsGromov-Hausdorff distanceReeb graphmetric distortionco-rank of the fundamental group

Mathematics Subject Classification ID

Paths and cycles (05C38) Real-valued functions on manifolds (58C05)

Related Items (7)

Criterion for a graph to admit a good orientation in terms of leaf blocks ⋮ Reeb graphs of circle-valued functions: a survey and basic facts ⋮ Reeb spaces of smooth functions on manifolds II ⋮ Realization of a digraph as the Reeb graph of a Morse-Bott function on a given surface ⋮ Combinatorial modifications of Reeb graphs and the realization problem ⋮ Morse-Bott functions with two critical values on a surface ⋮ A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kronrod-Reeb graphs of functions on noncompact two-dimensional surfaces. I
• On representation of the Reeb graph as a sub-complex of manifold
• The convexity radius of a Riemannian manifold
• On fundamental groups of quotient spaces
• Sur l'unique ergodicité des 1-formes fermées singulières. (Unique ergodicity of closed singular 1-forms)
• Singular points of a Morsian form and foliations
• Combinatorial group theory.
• Maximal isotropic subspaces of skew-symmetric bilinear mapping
• Loops in Reeb graphs of \(n\)-manifolds
• Kronrod-Reeb graphs of functions on noncompact two-dimensional surfaces. II
• Realization of a graph as the Reeb graph of a Morse function on a manifold
• Loops in Reeb graphs of 2-manifolds
• Gromov-Hausdorff approximation of filamentary structures using Reeb-type graphs
• Reeb graphs for shape analysis and applications
• Level Sets on Disks
• Topological classification of simple Morse Bott functions on surfaces
• Volumes of balls in Riemannian manifolds and Uryson width
• EQUATIONS IN A FREE GROUP
• On the structure of a Morse form foliation
• THE FUNDAMENTAL GROUP OF THE HAWAIIAN EARRING IS NOT FREE
• Riemannian Geometry
• On graph approximations of surfaces with small area
• ON SYSTEMS OF EQUATIONS IN A FREE GROUP
• Isotropy index for the connected sum and the direct product of manifolds
• Cut numbers of 3-manifolds
• Local estimate on convexity radius and decay of injectivity radius in a Riemannian manifold
• Number of minimal components and homologically independent compact leaves for a morse form foliation
• The number of split points of a Morse form and the structure of its foliation
• The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
• A Few Snapshots from the Work of Mikhail Gromov
• An invitation to Morse theory
• The co-rank conjecture for 3-manifold groups

This page was built for publication: Approximation of metric spaces by Reeb graphs: Cycle rank of a Reeb graph, the co-rank of the fundamental group, and large components of level sets on Riemannian manifolds