Suppose I have two singular chains from the $n$-simplex into itself, $$\sigma, \tau: \Delta^n \to \Delta^n$$ and that I know that these are boundaries, $\sigma = \partial s$ and $\tau = \partial t$ for some $s, t: \Delta^{n+1} \to \Delta^n.$ What can I say about the composition $\sigma \circ \tau$? Is that a boundary?
2026-03-30 09:49:41.1774864181
Is the composition of chain boundaries a boundary?
58 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 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 HOMOLOGICAL-ALGEBRA
- How does $\operatorname{Ind}^G_H$ behave with respect to $\bigoplus$?
- Describe explicitly a minimal free resolution
- $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$
- Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective
- Group cohomology of $\mathrm{GL}(V)$
- two maps are not homotopic equivalent
- Existence of adjugant with making given natural transformation be the counit
- Noetherian property is redundant?
- What is the monomorphism that forms the homology group?
- Rational points on conics over fields of dimension 1
Related Questions in SIMPLEX
- Simplex Algorithm: basic solutions - optimal solution
- Homotopy type of simplicial complexes
- Face map not well-defined on oriented simplices
- Linear Programming: What is the rationale behind the Gauss Jordan Row operations we do after determining the leaving and entering variables?
- "No two values are the same" constraint in linear programming
- Optimal solution in Duplex simplex method
- How to add regularization to simplex solver
- Linear Optimization: Duality in Simplex
- Finding the vertices of linear image of the $n$-simplex
- Formulating LPP from given optimal table in Simplex method
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?