四元数线丛的Kreck-Stolz不变量
Kreck-Stolz invariants for quaternionic line bundles
摘要：
我们推广了Kreck-Stolz不变量s_2和s_3，定义了一个新的不变量，即t-不变量，用于4k-1维闭自旋流形M上的四元数线丛E，其中H^3（M; \Q）= 0，使得c_2（E）\in H^4（M）是挠的。t-不变量将闭光滑定向的2-连通有理同调7-球面分类到几乎同同态，即同同态到与奇异球面的连通和。它还检测奇异同胚之间的流形。t-不变量也给出了关于固定流形上四元数线丛的信息，我们用它给出了Feder和Gitler关于HP^k上四元数线丛的第二类Chern值的一个定理的新证明。S^{4k-1}的t-不变量与（4k-5）-茎上的Adams e-不变量密切相关。
英文摘要：
We generalise the Kreck-Stolz invariants s_2 and s_3 by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spin-manifolds M of dimension 4k-1 with H^3(M; \Q) = 0 such that c_2(E)\in H^4(M) is torsion. The t-invariant classifies closed smooth oriented 2-connected rational homology 7-spheres up to almost-diffeomorphism, that is, diffeomorphism up to connected sum with an exotic sphere. It also detects exotic homeomorphisms between such manifolds. The t-invariant also gives information about quaternionic line bundles over a fixed manifold and we use it to give a new proof of a theorem of Feder and Gitler about the values of the second Chern classes of quaternionic line bundles over HP^k. The t-invariant for S^{4k-1} is closely related to the Adams e-invariant on the (4k-5)-stem.
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