Haochen Qiu

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20242026

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5 papers · 1 filter

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--OzsvÃ¡th--SzabÃ³ 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 $3$ -sphere in the neck of two $K 3$ 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 $4$ -manifolds obtained through…

math.GT2024

Exotic diffeomorphisms on $4$ -manifolds with $b_{2}^{+} = 2$

Haochen Qiu

While the exotic diffeomorphisms turned out to be very rich, we know much less about the $b_{2}^{+} = 2$ case, as parameterized gauge-theoretic invariants are not well defined. In this…

math.GT2024

A surgery formula for Seiberg-Witten invariants

Haochen Qiu

We prove a surgery formula for the ordinary Seiberg-Witten invariants of smooth $4$ -manifolds with $b_{1} = 1$ . Our formula expresses the Seiberg-Witten invariants of the manifold aft…

Monopole triangle over integers

The Dehn twist on a connected sum of two homology tori

Surgery formulas for Seiberg-Witten invariants and family Seiberg-Witten invariants

Exotic diffeomorphisms on 4-manifolds with b2+​=2

A surgery formula for Seiberg-Witten invariants

Exotic diffeomorphisms on $4$ -manifolds with $b_{2}^{+} = 2$