arXiv subjects
Publications and source records attributed to Sudeep Podder.
In this article, we introduce the notion of $\mathcal P$-triviality of topological manifolds and give a complete description of the $\mathcal P$-triviality of stunted real and complex projective spaces.
In this note, we compute the upper characteristic rank of the projective Stiefel manifolds over $\mathbb{R}, \mathbb{C}$ and $\mathbb{H}$ and the flip Stiefel manifolds. We also provide bounds for the $\mathrm{cup}$ lengths of these spaces. We also provide necessary conditions for the existence of $S^3$-map between quaternionic Stiefel manifolds using the Fadell-Husseini index.
Let $\mathrm E_6$ denote the simply-connected compact exceptional Lie group of rank 6. The Lie group $\mathrm Spin(10)$ naturally embeds in $\mathrm E_6$, corresponding to the inclusion of the Dynkin diagrams. We determine the K-ring of the coset space ${\mathrm E}_6/\mathrm Spin(10)$. We identify the class of the tangent bundle of ${\mathrm E}_6/\mathrm Spin(10)$ in $KO({\mathrm E}_6/\mathrm Spin(10))$. As an application we show that ${\mathrm E}_6/\mathrm Spin(10)$ can be immersed in the Euclidean space $\mathbb R^{53}$.
Let $G_{n,k}$ denote the real Grassmann manifold of $k$-dimensional vector subspaces of $\mathbb R^n$. Using the Hodgkin spectral sequence, we compute the complex $K$-ring of $G_{n,k}$, up to a small indeterminacy, for all values of $n,k$ where $2\le k\le n-2$. When $n\equiv 0\!\!\mod 4, k\equiv 1\!\!\mod 2$ our result is complete.