# Questions tagged [spin-geometry]

For questions about spin manifolds, the groups $\operatorname{Spin}(n)$, as well as generalisations such as $\operatorname{Pin}(n)$ and $\operatorname{Spin}^c(n)$. This tag should also be used for any questions about the geometry of spin manifolds, including questions involving Dirac operators and the Lichnerowicz formula.

**1**

**0**answers

### First Chern Class of Contact Structure which is not Torsion

**9**

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### An equivalent definition for $\text{Spin}^c$-structures

**2**

**0**answers

### Existence of a certain kind of compact spin manifold with boundary

**6**

**0**answers

### Arf-Brown-Kervaire invariant and a surjective map $G \to Pin^-$

**9**

**1**answer

### Discrete Pin structures

**4**

**1**answer

### Spin groups in terms of matrices and/or linear operators

**5**

**0**answers

### Spinor representation for $\operatorname{Spin}(V \oplus V^*)$

**5**

**2**answers

### Lifting a diffeomorphism into a spinor bundle automorphism

**2**

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### Inflation of $w_j(V_{SO(N)})$ and $w_j(M)$ from $SO(N)$ to $Spin(N)$ or Spin geometry

**2**

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### The complex Clifford algebra

**3**

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### Pairing the Arf with Stiefel-Whitney class

**2**

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### A generalization of the Clifford algebra

**3**

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### The Dirac-Ricci operator

**3**

**0**answers

### About mod 2 Index of Dirac Operators in 3D on Non-Orientable Manifold

**0**

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### The generalized Seiberg-Witten equations

**2**

**0**answers

### Is there an analog of a Chern-Simons formula for the pfaffian $Pf(F)$ of a $SO(2n)$ curvature $F$?

**12**

**1**answer

### Obstruction of spin-c structure and the generalized Wu manifods

**9**

**3**answers

### Spin-H structures

**8**

**0**answers

### Are spin Hurwitz numbers $r$-spin Hurwitz numbers?

**1**

**1**answer

### Example of a certain partitioned manifold

**7**

**1**answer

### What is a formal definition of a Fermionic quantum field?

**3**

**2**answers

### $spin_{\mathbb{C}}$ Connection and Charge Parity

**7**

**0**answers

### Vanishing of K-theoretic index and positive scalar curvature

**6**

**1**answer

### Lickorish-Wallace theorem for torsion spin$^c$ 3-manifolds?

**3**

**0**answers

### Noncompact dual of $\mathrm{Spin}(2n)$ corresponding to $\mathfrak{so}^*(2n)$

**3**

**0**answers

### Causal fermion systems fromm fractal geometry

**6**

**1**answer

### Spinor bundle tensored with certain line bundle gives the dual spinor bundle

**7**

**1**answer

### First Chern class of a specific line bundle

**6**

**1**answer

### Action of the spin covariant derivative on gamma matrices?

**16**

**1**answer

### An orientable non-spin${}^c$ manifold with a spin${}^c$ covering space

**3**

**1**answer

### Injectivity of the $\alpha$-genus

**8**

**0**answers

### Dixmier-Douady class is the third integral Stiefel-Whitney class

**3**

**1**answer

### Spin Structure on AdS- Schwarzschild manifold

**6**

**0**answers

### Has the structure of the 2-dimensional pin$^{\pm}$ bordism categories been written down?

**3**

**0**answers

### Section of the spinor bundle over $S^{1}$ that extend to sections of the spinor bundle over $D^{2}$

**8**

**1**answer

### K-homology classes of Dirac operators on Hermitian manifolds

**8**

**0**answers

### Regularilty of Commutative Spectral Triples

**6**

**0**answers

### Sections of “forgetful” projections between flag manifolds

**2**

**2**answers

### Matrix expression for elements of $\text{SO}_0(1,4)$

**9**

**1**answer

### Is a 4-dimensional submanifold of a spin manifold always spin?

**12**

**1**answer

### Spin structures on Sasakian manifolds and the Kähler analogy

**2**

**0**answers

### Understanding the relationship between Spin$^c$ orientations and Spin$^c$ structures

**3**

**1**answer

### Lagrangian Grassmannian as a Spin Manifold

**5**

**1**answer

### Which Kahler Manifolds Are Spin?

**2**

**1**answer

### Trace of the chiral matrix of a subspace

**3**

**1**answer

### Recovering K-theory and KO-theory from KR-theory and Bott Periodicity Theory

**5**

**1**answer

### Topological obstruction for the existence of spin$^c$ structure

**7**

**2**answers

### Pin$^+$ and Pin$^−$ structure for manifolds in any dimensions

**-1**

**3**answers

### natural embedding $V \to Cl(V,q)$ [closed]

**4**

**0**answers