PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
April 13, 2026Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas0 citationsOpen Access

Morse–Bott inequalities for endomorphisms

EMEnrique Macías-VirgósAMAlejandro O. Majadas-MoureDMDavid Mosquera-Lois

Key Points

  • The aim is to establish inequalities that relate the dynamics of simplicial maps and discrete Morse–Bott functions.
  • Defined a simplicial complex K and a simplicial map g: K → K.
  • Invested discrete Morse–Bott functions under a specific condition involving g and simplices σ.
  • Established a set of inequalities generalizing known Morse–Bott inequalities.
  • Showed that the inequalities hold for all simplices σ in K.
  • Recovered classical Morse–Bott inequalities for the case where g is the identity.

Abstract

Abstract Let K be a finite simplicial complex, let g: K K g: K → K be a simplicial map and let f be a discrete Morse–Bott function on K satisfying f (g () ) f () f (g (σ) ) ≤ f (σ) for all simplices σ in K. We establish a set of inequalities (generalizing the Morse–Bott inequalities which we recover as a particular case when g is the identity) relating the dynamics of g and f.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Macías-Virgós et al. (2026) studied this question.

synapsesocial.com/papers/69dc88583afacbeac03ea310https://doi.org/10.1007/s13398-026-01858-w
Ask AI
Helpful
Bookmark
Share
View Full Paper

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Discrete Morse theory for open complexes2024
  2. 2Connecting Discrete Morse Functions via Birth-Death Transitions2025
  3. 3Morse Decompositions on Flag Bundles and Uniform Bounds of Cocycles2026
  4. 4Morse–Bott cohomology from homological perturbation theory2024 · 3 citations
  5. 5Stability of the morse index for the p-harmonic approximation of harmonic maps into homogeneous spaces2026