Almost Complex Structures on Homotopy Complex Projective Spaces

2022/01/18 by Keith Mills, Mills, Keith
Mathematics · #19L64 (Secondary) #32Q60 #57R15 (Primary) 57R20 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2201.07176

openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that all homotopy ℂPⁿs, smooth closed manifolds with the oriented homotopy type of ℂPⁿ, admit almost complex structures for 3 ≤ n ≤ 6, and classify these structures by their Chern classes. Our methods provide a new proof of a result of Libgober and Wood on the classification of almost complex structures on homotopy ℂP⁴s.

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