I can't manage to calculate the homology and comology groups of the Grassmannian $G(k+1,n+1)$. I know the definition of homology group and I read which are the homology groups of a Grassmannian, but I can't understand how to get those groups. Can anyone help me?
2026-03-26 00:53:34.1774486414
Homology groups of a Grassmannian
481 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRAIC-GEOMETRY
- How to see line bundle on $\mathbb P^1$ intuitively?
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- An irreducible $k$-scheme of finite type is "geometrically equidimensional".
- Global section of line bundle of degree 0
- Is there a variant of the implicit function theorem covering a branch of a curve around a singular point?
- Singular points of a curve
- Find Canonical equation of a Hyperbola
- Picard group of a fibration
- Finding a quartic with some prescribed multiplicities
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 GRASSMANNIAN
- Reference for Grassmannian Manifold
- Minimization over constrained projection matrices
- A smooth map from $Gr_{\mathbb{C}} (1,2)$ to $Gr_{\mathbb{R}} (2,4)$
- Bundles on Grassmannians
- How can I find the subspace basis most "aligned" to the ambient space axes?
- Generically rebuilding non-degenerate matrices from a vector
- Iwasawa decomposition for real Grassmannians
- Schubert variety associated to a flag of subspaces of a vector space
- Definition of k-plane as linear subspace of dim. k?
- Grassmannian $G(2,3)$ homeomorphic to the projective plane $\mathbb{P}_{\mathbb{R}}^2$
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?