I know what a definition of a vector bundle (line bundle) is, but in the papers I am currently working on, they use the term $G$-vector bundle, where $G$ is a group.
Can somebody explain what this means?
Thanks in advance!
2026-03-29 08:44:58.1774773898
Vector bundles and groups
42 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in DIFFERENTIAL-GEOMETRY
- Smooth Principal Bundle from continuous transition functions?
- Compute Thom and Euler class
- Holonomy bundle is a covering space
- Alternative definition for characteristic foliation of a surface
- Studying regular space curves when restricted to two differentiable functions
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- Regular surfaces with boundary and $C^1$ domains
- Show that two isometries induce the same linear mapping
- geodesic of infinite length without self-intersections
Related Questions in DEFINITION
- How are these definitions of continuous relations equivalent?
- If a set is open, does it mean that every point is an interior point?
- What does $a^b$ mean in the definition of a cartesian closed category?
- $\lim_{n\to \infty}\sum_{j=0}^{[n/2]} \frac{1}{n} f\left( \frac{j}{n}\right)$
- Definition of "Normal topological space"
- How to verify $(a,b) = (c,d) \implies a = c \wedge b = d$ naively
- Why wolfram alpha assumed $ x>0$ as a domain of definition for $x^x $?
- Showing $x = x' \implies f(x) = f(x')$
- Inferior limit when t decreases to 0
- Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?
Related Questions in VECTOR-BUNDLES
- Compute Thom and Euler class
- Confusion about relationship between operator $K$-theory and topological $K$-theory
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- Why is the index of a harmonic map finite?
- Scheme theoretic definition of a vector bundle
- Is a disjoint union locally a cartesian product?
- fiber bundles with both base and fiber as $S^1$.
- Is quotient bundle isomorphic to the orthogonal complement?
- Can We understand Vector Bundles as pushouts?
- Connection on a vector bundle in terms of sections
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Any fiber bundle (no matter whether the fiber is a vector space or not) has a structure group, which is the group of all transformations that could arise in the transition maps.
A $G$-bundle is a bundle where the transition maps have to be elements of $G$. It follows that $G$ must act on the fiber, in a way that is made explicit beforehand. Where the fibers are vector spaces, it is required that transition maps preserve that structure, and therefore the structure group is a subgroup of $GL(n,\Bbb k)$.