Does anyone know where I can find a good proof for the basis theorem of the cohomology ring of the Grassmannian, or give me a sketch of the proof? I'm already familiar with basic Schubert Calculus.
2025-01-13 07:44:24.1736754264
Basis theorem for the Grassamannian
65 Views Asked by Alessandro https://math.techqa.club/user/alessandro/detail At
1
There are 1 best solutions below
Related Questions in ALGEBRAIC-TOPOLOGY
- Proper and discontinuous action of a group
- Euler Characteristic of a boundary of a Manifold
- Rank of fundamental groups of open subsets.
- Is it true that Morse function on non-trivial knot has at least 4 critical points?
- What are the exact critera for a CW-complex being a polytope?
- Subspace of a compactly generated space?
- Triangle inequality of hyperbolic metric
- Connect Sum of a connected, compact manifold of dimension n and $S^n$
- Proof of : "Signature of $\mathbb{C}P^{2n}$ is $1$"
- Equality $H^i(K,\mathcal{F}_{|K})=\varinjlim_{U\supset K}H^i(U,\mathcal{F}_{|U})$ for a constructible sheaf
Related Questions in HOMOLOGY-COHOMOLOGY
- Proof of : "Signature of $\mathbb{C}P^{2n}$ is $1$"
- Equality $H^i(K,\mathcal{F}_{|K})=\varinjlim_{U\supset K}H^i(U,\mathcal{F}_{|U})$ for a constructible sheaf
- Question about Gysin map (pushforward in cohomology)
- Why are simplicial complexes modules?
- Computing real de Rham cohomology of Hironaka's 3-manifold example
- Simpler way of computing the first homology group of $\Delta^4$ (without the interior)?
- First Cohomology group trivial for a simply connected manifold?
- Faulty Argument: Chern number of U(1)-bundle over $T^2$ is zero?
- About rational Hodge conjecture.
- Homotopic vs. homologous simplices/chains
Related Questions in GRASSMANNIAN
- Why is the dimension of this Grassmann manifold $G_{d, n}$ equal to $(d+1)(n-d)$ formed by the Plucker coordinates of a $d$-plane?
- Isoclinic rotations in four dimensions
- Construction of Grassmann manifolds
- Full flag $Fl_{\mathbb C}(3)$
- Direct Limit of Grassmannians
- Generalized Gauss map, giving rise to second fundamental form
- Schubert decomposition of a Grassmannian
- The oriented Grassmannian $\widetilde{\text{Gr}}(k,\mathbb{R}^n)$ is simply connected for $n>2$
- Trying to understand some basic facts about tangent space of Grassmannian.
- Can the cohomology of the Grassmannian identified with the cohomology of a specific dense open subvariety?
Related Questions in SCHUBERT-CALCULUS
- Schubert Cells of Flags
- Schubert cell decomposition and full flags
- Schubert decomposition of a Grassmannian
- The associated Schubert variety of a flag of subspaces of a vector space.
- Applying the divided difference operator
- Smoothness of Schubert Variety
- closure of a Schubert cell
- Schubert cycles that intersect generically transversely.
- Elementary description for $\mathbb{P}^1\times X$ and rational equivalence
- Generically transversally intersecting Schubert cycles
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity
In "Characteristic Classes" Milnor and Stashev calculate the $\mathbb{F}_2$ cohomology of $BO(n)$ and $BO$ and the integral cohomology of $BU(n)$ and $BU$. The approach is to give a CW decomposition which is enough for the latter and for the former you use characteristic class argument to argue that all the coboundary maps are trivial.