Covering action on Conley index theory

DOI10.1017/etds.2022.13OpenAlexW4213243520WikidataQ114118637 ScholiaQ114118637MaRDI QIDQ5889847

Dahisy V. de S. Lima, Ewerton R. Vieira, Unnamed Author

Publication date: 27 April 2023

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.04929

zbMATH Keywords

Conley indexNovikov complexcovering spaceconnection matrixcircle-valued function

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Index theory for dynamical systems, Morse-Conley indices (37B30) Coverings in algebraic geometry (14E20) Variational aspects of group actions in infinite-dimensional spaces (58E40)

Cites Work

• Formal Laurent series in several variables
• Generalized topological transition matrix
• Connection matrices for Morse-Bott flows
• Rigidity and gluing for Morse and Novikov complexes
• Cancellations for circle-valued Morse functions via spectral sequences
• Zeta functions, periodic trajectories, and the Conley index
• Isolating neighborhoods and chaos
• The Morse-Witten complex via dynamical systems
• Index Filtrations and the Homology Index Braid for Partially Ordered Morse Decompositions
• The Connection Matrix Theory for Morse Decompositions
• The Connection Matrix in Morse-Smale Flows
• Morse Theory, the Conley Index and Floer Homology
• Connected Simple Systems and The Conley Index of Isolated Invariant Sets
• The Connection Map for Attractor-Repeller Pairs
• Transition matrix theory
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