3 papers
math.GT2026
Monopole triangle over integers
Haochen Qiu, Fan Ye
We prove the surgery exact triangle for monopole (Seiberg--Witten) Floer homology over integer coefficients, extending the work of Kronheimer--Mrowka--Ozsváth--Szabó over $\mathb…
math.GT2025
The Dehn twist on a connected sum of two homology tori
Haochen Qiu
Kronheimer-Mrowka shows that the Dehn twist along a -sphere in the neck of two surfaces is not smoothly isotopic to the identity. Their result requires that the manifolds a…
math.GT2024
Surgery formulas for Seiberg-Witten invariants and family Seiberg-Witten invariants
Haochen Qiu
We prove a surgery formula for the ordinary Seiberg-Witten invariants, and surgery formulas for the families Seiberg-Witten invariants of families of -manifolds obtained through…