# Questions tagged [connections]

Ehresmann connections; covariant derivatives; connections on vector bundles, principal bundles, ∞-bundles, submersions, bundle gerbes; holonomy and higher holonomy; parallel transport; torsion; curvature. See also the tags [principal-bundles], [vector-bundles], [gerbes], [curvature], [geodesics], [characteristic-classes], [torsion].

**3**

**1**answer

### Curvature of principal bundle

**2**

**0**answers

### Local coordinates of one form on a principal bundle

**5**

**1**answer

### Question about a proof in Berthelot's crystalline book

**0**

**0**answers

### Change in Connection on a complex Line bundle

**7**

**0**answers

### (Higher) flat connections and Grothendieck construction

**1**

**0**answers

### About irreducible connection

**1**

**1**answer

### Projectively flat connection

**2**

**1**answer

### Splitting of higher order jet sequence

**8**

**2**answers

### When do flat holomorphic connections exist?

**1**

**1**answer

### The notion of a “relatively” flat connection

**2**

**1**answer

### Solving the Airy equation by Borel summation

**4**

**1**answer

### Curvature as infinitesimal holonomy 2

**1**

**1**answer

### Flat connection of a degree zero line bundle on curve

**4**

**1**answer

### A de Rham space for meromorphic connections?

**17**

**2**answers

### A non-Abelian de Rham complex?

**1**

**0**answers

### Covariant Derivative of sections of a pullback bundle

**1**

**1**answer

### Yang-Mills over surfaces

**2**

**1**answer

### Almost geodesic on non complete manifolds

**40**

**5**answers

### What is the Levi-Civita connection trying to describe?

**1**

**0**answers

### Curvature of a superconnection

**3**

**2**answers

### Pullback of a connection

**6**

**0**answers

### Is there a contact instanton connection on the tangent bundle of the 5-sphere?

**4**

**4**answers

### Connections in the setting of algebraic geometry

**1**

**1**answer

### What is the natural Lie groupoid structure on the Atiyah Lie groupoid of a principal $G$-bundle?

**4**

**2**answers

### Katz's proof of Cartier's (descent) theorem

**2**

**1**answer

### Vector field along an immersion whose covariant derivative is the differential

**2**

**2**answers

### Integrability condition for flat connections

**1**

**0**answers

### Can logarithmic connection on holomorphic vector bundle induce logarithmic connection on dual bundle?

**3**

**0**answers

### Opers and global differential operators

**6**

**2**answers

### 1d TQFT minus connection =?

**4**

**1**answer

### history of geometric mechanics

**6**

**0**answers

### Examples of connection preserving maps in differential geometry

**2**

**1**answer

### Simple example of non-integrable holomorphic connection

**5**

**0**answers

### Hopf fibration extended to bundle over $\mathbb{C}^2$

**2**

**1**answer

### Characterisation of (integrable) connections on (trivial) principal bundle

**2**

**1**answer

### Canonical connection on $\mathcal{A}\times X$

**6**

**1**answer

### What is the definition of homotopy flat connections?

**6**

**0**answers

### Geometric theory for cohomology groups $H^p(M;\mathbb{Z})$

**-1**

**1**answer

### Connections on vector bundles over elliptic curves - concrete computations

**6**

**0**answers

### Foliated circle bundles whose Euler class is torsion

**1**

**0**answers

### Does holonomy determine parallel transport? [duplicate]

**2**

**0**answers

### Pullback connection and diffeomorphism of the base

**1**

**1**answer

### Katz's paper on $p$-curvature – help with proof understanding

**2**

**0**answers

### Solving equations of motion of holomorphic BF theory - pure gauge in complex coordinates

**1**

**1**answer

### Map from local systems to holomorphic line bundles on a curve

**5**

**0**answers

### A struggle with jets and Grothendieck vs Ehresmann connections

**1**

**0**answers

### One parameter change of a section of $T^*M \otimes End(TM)$ on an affinely flat manifold

**6**

**0**answers

### Is there an analog of the Levi–Civita connection for schemes?

**4**

**1**answer

### A consequence of Ambrose-Singer theorem on holonomy

**2**

**0**answers