AI 中文总结
本研究用Fukumoto-Furuta $w$-不变量刻画自旋Seifert 3-流形实Seiberg--Witten Floer同伦型的局部等价类，借助实轨形Bauer-Furuta不变量证明环面纽结对应覆叠的同伦型局部等价类最终周期，且相关协连同态线性无关。
AI 中文摘要
我们借助Fukumoto-Furuta $w$-不变量，刻画了带特定奇对合的自旋Seifert 3-流形的实Seiberg--Witten Floer同伦型的局部等价类。证明过程使用了由Fukumoto-Furuta-Ue构造的一类自旋4-轨形的实轨形Bauer-Furuta不变量。对于环面纽结，我们证明了与其$2^k$重循环分歧覆叠相关的实Floer同伦型的局部等价类在$k$趋于无穷时最终呈周期性。最后，我们证明了整数值协连同态$\{8δ_R^{(k)}\}_{k\geq1}$是线性无关的。
英文摘要
We express the local-equivalence classes of real Seiberg--Witten Floer homotopy types for spin Seifert $3$-manifolds with certain odd involutions in terms of the Fukumoto-Furuta $w$-invariant. The proof uses real orbifold Bauer-Furuta invariant for a class of spin $4$-orbifolds constructed by Fukumoto-Furuta-Ue. For torus knots, we prove that the local-equivalence classes of real Floer homotopy types associated with their $2^k$-fold cyclic branched covers are eventually periodic in $k$. Finally, we prove that the integer-valued concordance homomorphisms $\{8δ_R^{(k)}\}_{k\geq1}$ are linearly independent.
Comments34 pages, 2 figures
