As definition, the first Chern class is an element in $H^2_{dR}(S^2)$, how can we represent it as an integer? If we change the orientation of $S^2$, then does the integer change sign?
2026-03-27 03:44:17.1774583057
Chern class of Hopf fibration: $S^1 \hookrightarrow S^3 \xrightarrow{\ p \, } S^2$?
510 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRAIC-TOPOLOGY
- How to compute homology group of $S^1 \times S^n$
- the degree of a map from $S^2$ to $S^2$
- Show $f$ and $g$ are both homeomorphism mapping of $T^2$ but $f$ is not homotopy equivalent with $g.$
- Chain homotopy on linear chains: confusion from Hatcher's book
- Compute Thom and Euler class
- Are these cycles boundaries?
- a problem related with path lifting property
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- Cohomology groups of a torus minus a finite number of disjoint open disks
- CW-structure on $S^n$ and orientations
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
Related Questions in CHARACTERISTIC-CLASSES
- Passage in the proof of Chern-Weil method in John Roe's Elliptic operators book
- "Symmetry of trace" passage in the proof of Chern Weil.
- Proving that a form is horizontal in the Chern Weil method proof
- Chern-Weil homomorphism and Chern/Pontryagin/Euler class
- Chern classes, cohomology classes with real/integer coefficients
- prerequisite for reading characteristic classes
- On the proof of Poincaré dual of transversal intersection
- How does one introduce characteristic classes
- Applications of Chern class to gauge theories in physics
- First obstacle to triviality is orientability
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?