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Characteristic classes on certain quotients of Stiefel manifolds

Debanil Dasgupta

Abstract

In this paper, we calculate characteristic classes for certain quotients of real Stiefel manifolds $V_{n,k}$ and then derive results on certain numerical invariants, such as characteristic rank and skew embedding dimension, for those spaces.

Characteristic classes on certain quotients of Stiefel manifolds

Abstract

In this paper, we calculate characteristic classes for certain quotients of real Stiefel manifolds and then derive results on certain numerical invariants, such as characteristic rank and skew embedding dimension, for those spaces.
Paper Structure (13 sections, 12 theorems, 38 equations)

This paper contains 13 sections, 12 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Organization
  3. Computations for projective Stiefel manifolds
  4. Skew embeddings of $PV_{n,k}$
  5. Characteristic rank of projective Stiefel manifolds
  6. The complex case
  7. The circle quotient Stiefel manifolds
  8. The tangent bundle of $Y_{n,k}$
  9. ${\mathbb{Z}}_2$-cohomology of $Y_{n,k}$
  10. Computations for the circle quotient manifolds
  11. Stable span and paralleizability of $Y_{n,k}$
  12. Skew embedding and immersion dimensions of $Y_{n,k}$
  13. Characteristic rank of $Y_{n,k}$

Key Result

Theorem 2.1

Baralic2010 If $k:= \text{max}\{ i \mid \bar{w}_i(M) \neq 0 \}$, then $\bar{w}_{2k}(T(F_2(M)) \neq 0$ and hence $N(M)\geq 2n+2k+1 .$

Theorems & Definitions (21)

  • Theorem 2.1
  • Theorem 2.2
  • proof
  • Lemma 2.3
  • proof
  • Theorem 2.4
  • proof
  • Proposition 2.5
  • proof
  • Theorem 3.1
  • ...and 11 more