Almost complex structures on homotopy complex projective spaces
Copyright policy )Almost complex structures on homotopy complex projective spaces
We show that all homotopy $\mathbb{C}P^n$s, smooth closed manifolds with the oriented homotopy type of $\mathbb{C}P^n$, admit almost complex structures for $3 \leq n \leq 6$, 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 $\mathbb{C}P^4$s.
17 pages. Corrected error in previous version
Geometric applications of topological \(K\)-theory, Geometric Topology (math.GT), Almost complex manifolds, Specialized structures on manifolds (spin manifolds, framed manifolds, etc.), Mathematics - Geometric Topology, Characteristic classes and numbers in differential topology, geometric applications of topological \(\mathrm{K}\)-theory, FOS: Mathematics, Algebraic Topology (math.AT), almost complex manifolds, 57R15 (Primary) 57R20, 32Q60, 19L64 (Secondary), Mathematics - Algebraic Topology, characteristic classes and numbers in differential topology, special structures on manifolds
Geometric applications of topological \(K\)-theory, Geometric Topology (math.GT), Almost complex manifolds, Specialized structures on manifolds (spin manifolds, framed manifolds, etc.), Mathematics - Geometric Topology, Characteristic classes and numbers in differential topology, geometric applications of topological \(\mathrm{K}\)-theory, FOS: Mathematics, Algebraic Topology (math.AT), almost complex manifolds, 57R15 (Primary) 57R20, 32Q60, 19L64 (Secondary), Mathematics - Algebraic Topology, characteristic classes and numbers in differential topology, special structures on manifolds
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