Here is a very simple question that I can't seem to figure out for some reason. If we construct an Euler class as in Milnor's Characteristic classes, why is it that it behaves functorially (Naturality)? That is, why
$$e(F) = f^*e(E)?$$
2026-03-25 22:23:35.1774477415
If we construct an euler class, why is it that it behaves functoriality (Naturality)? That is:
193 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related 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 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
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?
By functoriality of cohomology and uniqueness (and existence) of the Thom Class presented in Thm 9.1. in Milnors Characteristic classes the naturality of the euler class follows. Just write down the commutative diagramm arising from the bundle map $f: F \to E$ (which also yields the map $(F,F_0) \to (E,E_0)$) and look where the Thom class goes and hence where the euler class is forced to go.