论文标题
同源性的Furuta-Ohta不变性的手术和切除
Surgery and Excision for Furuta-Ohta invariants on Homology $S^1 \times S^3$
论文作者
论文摘要
我们证明了手术配方和furuta-ohta不变的$λ_{fo} $的切除公式，在同源性$ s^1 \ times s^3 $上定义，该$提供了更多证据，以与Casson-Seiberg-seiberg-witter noftitter noftitter noftitter noftitter $λ_{sw} $。这些公式用于计算某些在$ 3 $ -MANIFOLDS下以绘图托里的映射托里的家族的$λ_{fo} $。在证据的过程中，我们在$ 4 $ - 同源性的$ 4 $ - manifolds $ h _*（d^2 \ times t^2; \ mathbb {z}）$上完整描述了ASD Instantons的学位 - 零模量空间，并使用圆柱末端建立在$ [0，\ infty）\ times \ times times times t^$ t^3 $上。
We prove a surgery formula and an excision formula for the Furuta-Ohta invariant $λ_{FO}$ defined on homology $S^1 \times S^3$, which provides more evidence on its equivalence with the Casson-Seiberg-Witten invariant $λ_{SW}$. These formulae are applied to compute $λ_{FO}$ of certain families of manifolds obtained as mapping tori under diffeomorphisms of $3$-manifolds. In the course of the proof, we give a complete description of the degree-zero moduli space of ASD instantons on $4$-manifolds of homology $H_*(D^2 \times T^2; \mathbb{Z})$ with a cylindrical end modeled on $[0, \infty) \times T^3$.
