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Mappings between balls · Question 1.5

Complexity of CR Mappings · AIMPL workshop record

MSC 32 · Several complex variables and analytic spaces

Editorial mapping of AIMPL source category: Several complex variables. http://aimpl.org/crmap/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Let f:Bn→BNf:\mathbb{B}^{n} \rightarrow \mathbb{B}^{N} be a proper rational map. Is ff homotopic to a polynomial map pp of the same degree? That is, ∀t∈[0,1]\forall t \in [0, 1], each ft:Bn→BNf_{t}:\mathbb{B}^{n} \rightarrow \mathbb{B}^{N} is proper with f0=ff_{0} = f and f1=pf_{1} = p.

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References
  1. [1]Complexity of CR Mappings · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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