Consider a base manifold $\mathcal{M}$ and a smooth bundle $E\to\mathcal{M}$. I am interested in the cohomology groups of the variational bicomplex associated with the jet bundle $J^{\infty}E$. In particular, if $d$ is the exterior derivative over $\mathcal{M}$ and $\delta$ is the variational derivative, given that we know the structure of $E$, what can we say about the cohomology of $J^{\infty}E$ induced by $\delta$?
2026-03-25 19:01:25.1774465285
Jet bundle cohomology
139 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DIFFERENTIAL-TOPOLOGY
- Getting a self-homeomorphism of the cylinder from a self-homeomorphism of the circle
- what is Sierpiński topology?
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- The regularity of intersection of a minimal surface and a surface of positive mean curvature?
- What's the regularity of the level set of a ''semi-nondegenerate" smooth function on closed manifold?
- Help me to prove related path component and open ball
- Poincarè duals in complex projective space and homotopy
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- Prove that the sets in $\mathbb{R}^n$ which are both open and closed are $\emptyset$ and $\mathbb{R}^n$
Related Questions in HOMOLOGY-COHOMOLOGY
- Are these cycles boundaries?
- Cohomology groups of a torus minus a finite number of disjoint open disks
- $f$ - odd implies $d(f)$ - odd, question to the proof
- Poincarè duals in complex projective space and homotopy
- understanding proof of excision theorem
- proof of excision theorem: commutativity of a diagram
- exact sequence of reduced homology groups
- Doubts about computation of the homology of $\Bbb RP^2$ in Vick's *Homology Theory*
- the quotien space of $ S^1\times S^1$
- Rational points on conics over fields of dimension 1
Related Questions in CLASSICAL-MECHANICS
- An underdetermined system derived for rotated coordinate system
- Bouncing ball optimization
- Circular Motion Question - fully algebraic
- How can I solve this pair of differential equations?
- How to solve $-\frac{1}{2}gt^2\sin \theta=x$ when $x$ equals $0$
- Find the acceleration and tension in pulley setup
- Derive first-order time derivatives in a second-order dynamic system
- Phase curves of a spherical pendulum
- Velocity dependent force with arbitrary power
- An explanation for mathematicians of the three-body problem using a simple example, and the moons of Saturn
Related Questions in FIBER-BUNDLES
- Coset and Fiber
- Examples of Lie algebra bundles and its application
- Induced fiber bundle equivalency
- The relation between $M$ is orientable and the normal bundle of $M$ in $\mathbb{R}^n$ is trivial?
- Second Stiefel-Whitney class and first Pontryagin class of total spaces of linear $S^2$ bundles over $S^4$
- Cohomology of projective bundle only depends on base and fiber?
- Fiber bundle over torus
- Locally trivial bundle with fiber $O(n-1)$
- Odd cohomology of fibre bundles
- Projective space and sections inducing the same homology morphisms
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?