Morsifications and mutations

Abstract

We describe and investigate a connection between the topology of isolated singularities of plane curves and the mutation equivalence, in the sense of cluster algebra theory, of the quivers associated with their morsifications.

v3: Major revision and expansion, with several new results. v4: minor edits. 80 pages, 66 figures. Final version, to appear in J. Lond. Math. Soc

References in corpus (5)

• Total positivity, Grassmannians, and networks
• Algebraic functions and closed braids
• Cluster varieties from Legendrian knots
• Introduction to Cluster Algebras. Chapters 1-3
• Counting cluster-tilted algebras of type $A_n$

Cited by in corpus (11)

• Domain wall formation and magnon localization in twisted chromium trihalides
• Critical varieties in the Grassmannian
• KP theory, plabic networks in the disk and rational degenerations of M--curves
• Real regular KP divisors on $\mathtt{M}$-curves and totally non-negative Grassmannians
• A Lagrangian filling for every cluster seed
• Singularities and clusters
• Honda-Huang's work on contact convexity revisited
• Conic singularities and immediate transversality
• The Kashaev Equation and Related Recurrences
• Milnor fibration, A'Campo's divide and Turaev's shadow
• Complexity of quiver mutation equivalence