2 papers
math.GT2025
A Morse complex for the homology of vanishing cycles
Aleksander Doan, Juan Muñoz-Echániz
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are gen…
math.SG2025
Pseudo-holomorphic curves with a fixed complex structure in positive symplectic manifolds
Alessio Cela, Aleksander Doan
We prove a symplectic version of a conjecture of Lian and Pandharipande: in sufficiently high degree, the fixed-domain Gromov-Witten invariants of positive symplectic manifolds are…