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See searches and references containing SPINC STRUCTURE!SPINC STRUCTURE
Special tangential structure
In spin geometry, a spinc structure (or complex spin structure) is a generalization of a spin structure. In mathematics, these are used to describe spinor
Spinc_structure
4-manifold invariants
spin structure on M is a reduction of the structure group to Spinc, i.e. a lift of the SO(4) structure on the tangent bundle to the group Spinc. By a
Seiberg–Witten_invariants
Concept in differential geometry
manifold carries a spinC structure at all, the set of spinC structures forms an affine space. Moreover, the set of spinC structures has a free transitive
Spin_structure
Twisted spin group
{\displaystyle \mathbb {C} } . An important application of spinc groups is for spinc structures, which are central for Seiberg–Witten theory. The spin group
Spinc_group
Symplectic topology tool
homology is a homology theory for smooth 3-manifolds (equipped with a spinc structure). It may be viewed as the Morse homology of the Chern–Simons–Dirac
Floer_homology
Non-tensorial representation of the spin group
symplectic manifold) has a Spinc structure. Likewise, every complex vector bundle on a manifold carries a Spinc structure. A number of Clebsch–Gordan
Spinor
Special tangential structure
third rank.[citation needed] Every spin and even every spinc structure induces a spinh structure. Reverse implications don't hold as the complex projective
Spinh_structure
Superconductivity theory
constant section. When the manifold is four-dimensional, possessing a spinc structure, then one may write a very similar functional, the Seiberg–Witten functional
Ginzburg–Landau_theory
spinh manifold which doesn't allow a spinc structure. The latter property comes from the fact, that a spinc structure implies a vanishing third Stiefel-Whitney
Wu_manifold
Construction for vector bundles
spaces. Determinant line bundles naturally arise in four-dimensional spinc structures and are therefore of central importance for Seiberg–Witten theory.
Determinant_line_bundle
Glacial valley and monastic settlement in County Wicklow, Ireland
The Spinc (from the Irish "An Spinc"; meaning "pointed hill"), which overlooks the upper lake and the Glendalough valley below. The most noted Spinc trail
Glendalough
Set of topological invariants
Stiefel–Whitney class is zero) if and only if the bundle admits a spinc structure. All the Stiefel–Whitney numbers (see below) of a smooth compact manifold
Stiefel–Whitney_class
Gradient flow of the Seiberg–Witten action functional
compact orientable Riemannian 4-manifold. Every such manifold has a spinc structure, which is a lift of the classifying map f : M → BSO ( 4 ) {\displaystyle
Seiberg–Witten_flow
Study of vector bundles, principal bundles, and fibre bundles
\psi } . In this case the four-manifold must admit a SpinC structure, which defines a principal SpinC bundle P {\displaystyle P} with determinant line bundle
Gauge_theory_(mathematics)
Four-dimensional complete Riemannian manifold satisfying the vacuum Einstein equations
well-defined Dirac spinors. That is, it is not a spin structure. It can be given a spinc structure, however. The Page space, which exhibits an explicit
Gravitational_instanton
Connects homology and cohomology groups for oriented closed manifolds
generalized notion of orientability for that theory. For example, a spinC-structure on a manifold is a precise analog of an orientation within complex
Poincaré_duality
Moduli space of the Seiberg–Witten equations
2 T ∗ M ) {\displaystyle g\in \Gamma ^{\infty }(S^{2}T^{*}M)} and spinc structure s : M → BSpin c ( 4 ) {\displaystyle {\mathfrak {s}}\colon M\rightarrow
Seiberg–Witten_moduli_space
\operatorname {Spin} ^{\mathrm {c} }(M)\rightarrow H^{2}(M,\mathbb {Z} )} of spinc structures with a non-vanishing Seiberg–Witten invariant) and their Kronheimer–Mrowka
Kronheimer–Mrowka_basic_class
Algebra based on a vector space with a quadratic form
important is the link to a spin manifold, its associated spinor bundle and spinc manifolds. Clifford algebras have numerous important applications in physics
Clifford_algebra
Double cover Lie group of the special orthogonal group
symmetries of (electrically neutral, uncharged) fermions. Its complexification, Spinc, is used to describe electrically charged fermions, most notably the electron
Spin_group
operators, conformal Laplacians, spinorial Laplacians and Dirac operators on SpinC manifolds, systems of Dirac operators, the Paneitz operator, Dirac operators
Clifford_analysis
Generators of the Clifford algebra for relativistic quantum mechanics
\mathrm {Spin} (n)} . The complexification of the spin group, called the spinc group S p i n C ( n ) {\displaystyle \mathrm {Spin} ^{\mathbb {C} }(n)}
Gamma_matrices
205-square-kilometre (51,000-acre) protected area in Ireland
is Glendalough, which features a collection of Early Medieval monastic structures associated with St Kevin, a hermit priest. Other sites include the Education
Wicklow Mountains National Park
Wicklow_Mountains_National_Park
Dutch mathematician (1942–2010)
Duistermaat, J. J. (2011), The heat kernel Lefschetz fixed point formula for the Spinc dirac operator, Boston: Birkhäuser, ISBN 978-0-8176-8247-7; Duistermaat
Hans_Duistermaat
Headland in Ireland
built on the headland. The original lighthouse actually consisted of two structures to differentiate between Hook Head Lighthouse to the South in Wexford
Wicklow_Head
Twisted spin group
_{k}\operatorname {SO} (n)\times \pi _{k}(S^{3})} for k ≥ 2 {\displaystyle k\geq 2} . Spinc group Christian Bär (1999). "Elliptic symbols". Mathematische Nachrichten
Spinh_group
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