标题： 双复数极加权齐次多项式 显示英文标题

标题： Bicomplex polar weighted homogeneous polynomials

摘要： 我们研究了用双复变量及其共轭表达的实多项式映射$\mathbb{R}^{4n} \longrightarrow \mathbb{R}^{4}$的拓扑结构，这些多项式被称为双复混合多项式。 我们引入了极幂同质性的概念，这是一种推广复数环境下加权同质性性质的属性。 这导致了全局和球面 Milnor 纤维化的存在。 此外，我们讨论了双复向量微积分、Milnor 纤维化定理的双复全纯类比以及一种 Join 型定理，该定理描述了某些关于可分离变量的多项式纤维的同伦类型。 这扩展了之前关于复变量及其共轭的混合多项式的相关工作。 显示英文摘要

摘要： We study the topology of real polynomial maps $\mathbb{R}^{4n} \longrightarrow \mathbb{R}^{4}$ expressed in terms of bicomplex variables and their conjugates, which we refer to as bicomplex mixed polynomials. We introduce the notion of polar weighted homogeneity, a property that generalizes the concept of weighted homogeneity in the complex setting. This leads to the existence of global and spherical Milnor fibrations. Moreover, we include a discussion on bicomplex vector calculus, a bicomplex holomorphic analogue of the Milnor fibration theorem, and a theorem of Join type that describes the homotopy type of the fibers of certain polynomials on separable variables. This extends previous works on mixed polynomials in complex variables and their conjugates.