\(\text{Spin}^c\)-structures and \(S^1\)-actions

DOI10.1007/BF01390060zbMath0395.57020MaRDI QIDQ1253043

Akio Hattori

Publication date: 1978

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142582

zbMATH Keywords

Almost Complex StructureAtiyah-Singer FormulaChern ClassClosed Connected Oriented Differentiable Manifold of Dimension 2nCohomology Complex Projective SpacesDirac OperatorPontrjagin ClassS1- ActionSpinc-StructuresStiefel-Whitney Class

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Compact Lie groups of differentiable transformations (57S15) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Compact groups of homeomorphisms (57S10)

Related Items (24)

An invitation to circle actions ⋮ Finite group actions on a homotopy complex projective spaces ⋮ Torus actions, fixed-point formulas, elliptic genera and positive curvature ⋮ Complex contact manifolds and \(S^{1}\) actions ⋮ Positive scalar curvature and Poincaré duality for proper actions ⋮ On a generalized Petrie's conjecture via index theorems ⋮ Positive scalar curvature on manifolds with fibered singularities ⋮ Dirac operators and symmetries of quasitoric manifolds ⋮ Almost complex structures on homotopy complex projective spaces ⋮ Equivariant index of Dirac operators ⋮ Generalized elliptic genera and Baker-Akhiezer functions ⋮ Rigidity and vanishing theorems for almost quaternionic manifolds ⋮ Rigidity and vanishing theorems for almost even-Clifford Hermitian manifolds ⋮ On the Determinant and the Holonomy of Equivariant Elliptic Operators ⋮ On a symplectic generalization of Petrie’s conjecture ⋮ Spin\(^{q}\) manifolds and \(S^{1}\) actions ⋮ Formal geometric quantization. III: Functoriality in the \(\mathrm{spin}^c\) setting ⋮ Torus actions of generalized odd type on oriented manifolds ⋮ Rigidity and vanishing theorems on ℤ/𝕜 Spin^{𝕔} manifolds ⋮ String^{𝑐} structures and modular invariants ⋮ Unitary toric manifolds, multi-fans and equivariant index ⋮ \(S^ 1\) actions with only isolated fixed points on almost complex manifolds ⋮ Group actions on quasi-symplectic manifolds ⋮ Homotopy complex projective spaces with \(Pin\)(2)-action

Cites Work

• Unnamed Item
• Unnamed Item
• On smooth semifree \(S^1\) actions on cohomology complex projective spaces
• A setting for smooth \(S^1\) actions with applications to real algebraic actions on \(P(\mathbb{C}^{4n})\)
• \(S^ 1\)-actions on cohomology complex projective spaces with three components of the fixed point sets
• Harmonic spinors
• Clifford modules
• The index of elliptic operators. III
• OBSTRUCTIONS TO THE EXISTENCE OFS¹-ACTIONS. BORDISM OF RAMIFIED COVERINGS
• Complex Structures on Real Vector Bundles
• Smooth 𝑆¹ actions on homotopy complex projective spaces and related topics
• Torus actions on homotopy complex projective spaces
• Smooth \(S^1\)-manifold in the homotopy type of \(CP^3\)

This page was built for publication: \(\text{Spin}^c\)-structures and \(S^1\)-actions