Totally Real Mappings and Independent Mappings
Howard Jacobowitz, Peter Landweber
TL;DR
This paper investigates the minimal target dimension N for smooth maps from n-dimensional manifolds to complex space, focusing on independent maps and totally real immersions, to understand their optimal embedding properties.
Contribution
It introduces the concepts of independent maps and totally real immersions, analyzing their existence and optimal dimensions for all manifolds of a given dimension.
Findings
Determined bounds for N in independent maps.
Established conditions for totally real immersions.
Compared the dimensions for different classes of maps.
Abstract
We consider two classes of smooth maps M^n\to C ^N. Definition. A map f:M^n\to C^N is called an independent map if df_1(p)\wedge...\wedge df_N (p)\neq 0. We are interested in the optimal value of N for all manifolds of dimension n for independent maps and also for totally real immersions.
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Taxonomy
TopicsAdvanced Topology and Set Theory