4 papers
math.GT2026
Multi-framed real monopole Floer theory
Jiakai Li
This paper constructs a framed real monopole Floer homology for three-manifolds with involutions, marked with multiple basepoints. The relative gradings of these Floer homologies d…
math.GT2024
Real monopoles and a spectral sequence from Khovanov homology
Jiakai Li
Given a based link , we define a "tilde"-version of real monopole Floer homology and prove an unoriented skein exact triangle. We show the Euler character…
math.GT2023
Monopole Invariants for Webs and Foams
Jiakai Li
We develop a package of monopole Floer-theoretic invariants for webs and foams using real Seiberg-Witten theory with orbifold singularities, based on Kronheimer and Mrowka's framew…
math.GT2022
Monopole Floer Homology and Real Structures
Jiakai Li
We define a "real" version of Kronheimer-Mrowka's monopole Floer homology for a 3-manifold equipped with an involution. As a special case, we obtain invariants for links via their…