The first Pontrjagin classes of homotopy complex projective spaces

TL;DR

This paper proves that for even-dimensional manifolds homotopy equivalent to complex projective space, the difference in their first Pontrjagin classes is divisible by 16, revealing a specific topological invariant relation.

Contribution

It establishes a divisibility property of the first Pontrjagin class difference for even-dimensional homotopy complex projective spaces, a new topological invariant relation.

Findings

Difference of first Pontrjagin classes divisible by 16 for even n

Topological invariant relation between homotopy complex projective spaces and standard CP(n)

Provides new insights into smooth manifold classification

Abstract

Let $M^{2n}$ be a closed smooth manifold homotopy equivalent to the complex projective space $\mathbb{C}P(n)$. The purpose of this paper is to show that when $n$ is even, the difference of the first Pontrjagin classes between $M^{2n}$ and $\mathbb{C}P(n)$ is divisible by 16.