a spinᶜ structure (or complex spin structure) is a special classifying map that can exist for orientable manifolds. Such manifolds are called spinᶜ manifolds...

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...

a spinC structure. When a manifold carries a spinC structure at all, the set of spinC structures forms an affine space. Moreover, the set of spinC structures...

spinʰ manifold, which doesn't allow a spinᶜ structure. The latter property comes from the fact, that a spinᶜ structure implies ta vanishing third Stiefel-Whitney...

{\displaystyle \mathbb {C} } . An important application of spinᶜ groups is for spinᶜ structures, which are central for Seiberg–Witten theory. The spin group...

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...

symplectic manifold) has a Spinc structure. Likewise, every complex vector bundle on a manifold carries a Spinc structure. A number of Clebsch–Gordan...

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...

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...

third rank.[citation needed] Every spin and even every spinᶜ structure induces a spinʰ structure. Reverse implications don't hold as the complex projective...

constant section. When the manifold is four-dimensional, possessing a spinc structure, then one may write a very similar functional, the Seiberg–Witten functional...

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...

generalized notion of orientability for that theory. For example, a spinC-structure on a manifold is a precise analog of an orientation within complex...

\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...

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...

symmetries of (electrically neutral, uncharged) fermions. Its complexification, Spinc, is used to describe electrically charged fermions, most notably the electron...

operators, conformal Laplacians, spinorial Laplacians and Dirac operators on SpinC manifolds, systems of Dirac operators, the Paneitz operator, Dirac operators...

important is the link to a spin manifold, its associated spinor bundle and spinc manifolds. Clifford algebras have numerous important applications in physics...

\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)}...

is Glendalough, which features a collection of Early Medieval monastic structures associated with St Kevin, a hermit priest. Other sites include the Education...

_{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...

built on the headland. The original lighthouse actually consisted of two structures to differentiate between Hook Head Lighthouse to the South in Wexford...

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...