Hadi Zare

Let $G(n):=O(n),U(n),Sp(n)$ and define $MTG(n)$ to be the Thom spectrum $BG(n)^{-\gamma_n}$ where $\gamma_n \rightarrow BG(n)$ is the universal $n$-plane bundle over $BG(n)$. We consider recent results of Kashiwabara and the speaker on the splitting of $MTG(n)$ and its consequences. Such splittings have two immediate consequences: computational consequences and conceptual consequences.
We shall discuss both of these consequences, and try to relate them to some other computations in the theory of immersions.
This is a part of an ongoing project with Takuji Kashiwabara from Institut Fourier, which part of it have been publicised recently.