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Based on a pair of cohomology operations on so called $\delta-2$-formalspaces, we construct the integral cohomology rings of the classifying spaces ofthe Lie groups $Spin(n)$ and $Spin^{c}(n)$. As applications, we introducecharacteristic classes for the reduced topological $K_{Spin}$ theory, determinethe ring of integral Weyl invariants of the group $Spin(n)$, and demonstratetheir usages in spin geometry.

The characteristic classes and Weyl invariants of Spinor groups