<we><edit> <!-- questions and answers -->
qa.quantum-algebra
finite-fields
terminology
matrices
computational-complexity
fourier-analysis
graph-theory
geometry
ra.rings-and-algebras
stochastic-calculus
ergodic-theory
sp.spectral-theory
soft-question
integration
galois-theory
real-analysis
mg.metric-geometry
ac.commutative-algebra
co.combinatorics
smooth-manifolds
modular-forms
big-list
fa.functional-analysis
higher-category-theory
cv.complex-variables
at.algebraic-topology
Concrete example of $\infty$-categories
higher-category-theory
at.algebraic-topology
ag.algebraic-geometry
mp.mathematical-physics
lo.logic
Cup product on flat fiber bundles vs cup product on the corresponding Serre spectral sequence
at.algebraic-topology
gt.geometric-topology
fibre-bundles
Persistent homology over the integers
at.algebraic-topology
applications
Can a planar tangle have an infinite number of input disks?
at.algebraic-topology
knot-theory
planar-algebras
Can the 2-complex associated to a finitely presented group be triangulated?
at.algebraic-topology
geometric-group-theory
Continuously varying the singularities of a vector field
at.algebraic-topology
gt.geometric-topology
smooth-manifolds
manifolds
Connection between Stalling's end theorem and Seifert-van Kampen Theorem
at.algebraic-topology
gr.group-theory
geometric-group-theory
Embedded homology sphere
at.algebraic-topology
gt.geometric-topology
Interpretation of the cohomology of compact lie groups and their classifying spaces in DAG?
ag.algebraic-geometry
at.algebraic-topology
rt.representation-theory
homotopy-theory
derived-algebraic-geometry
Could an inverse of (weak) Morse inequality exists in some special case?
dg.differential-geometry
at.algebraic-topology
gt.geometric-topology
morse-theory
index-theory
Plus construction considerations.
algebraic-k-theory
kt.k-theory-and-homology
homotopy-theory
at.algebraic-topology
Is this an $E_\infty$-algebra?
at.algebraic-topology
ct.category-theory
homotopy-theory
operads
higher-algebra
Is there any known lower bound on the dimension of sphere of origin?
reference-request
at.algebraic-topology
What is the cohomological dimension of the commutator subgroup of the pure braid group?
at.algebraic-topology
gr.group-theory
gt.geometric-topology
group-cohomology
braid-groups
Computing an explicit homotopy inverse for $B(*,H,*) \hookrightarrow B(*,G,G/H)$
at.algebraic-topology
group-cohomology
Atiyah's paper "Non-existent complex 6-sphere"
dg.differential-geometry
at.algebraic-topology
complex-geometry
kt.k-theory-and-homology
Sullivan conjecture for compact Lie groups
at.algebraic-topology
lie-groups
smooth-manifolds
classifying-spaces
Simplicial complex construction from given Betti numbers?
ag.algebraic-geometry
at.algebraic-topology
gn.general-topology
What is the current understanding regarding complex structures on the 6-sphere?
dg.differential-geometry
at.algebraic-topology
complex-geometry
kt.k-theory-and-homology
index-theory
Relationships between homology maps of cobordant manifolds
dg.differential-geometry
at.algebraic-topology
gt.geometric-topology
Covering maps in real life that can be demonstrated to students
at.algebraic-topology
big-list
covering-spaces
Plane Curve invariants via Contour Integrals
cv.complex-variables
at.algebraic-topology
A groupoid which is homotopy equivalent to $BG$
at.algebraic-topology
simplicial-stuff
Complexity of computing the Vietoris-Rips complex
at.algebraic-topology
computational-topology
Singularity of torus fixed points from combinatorial data
ag.algebraic-geometry
reference-request
co.combinatorics
at.algebraic-topology
sg.symplectic-geometry
Homology of a limit of spectra + Cofiber
at.algebraic-topology
homotopy-theory
stable-homotopy
chromatic-homotopy
Given a link $L\subset S^3$ how to construct a link $L'$ whose complement have hyperbolic structure?
at.algebraic-topology
gt.geometric-topology
knot-theory
hyperbolic-geometry
3-manifolds
Has the structure of the 2-dimensional pin$^{\pm}$ bordism categories been written down?
reference-request
at.algebraic-topology
ct.category-theory
tqft
spin-geometry
Why do we need model categories?
ag.algebraic-geometry
at.algebraic-topology
homotopy-theory
model-categories
Alexander modules and weight filtrations
ag.algebraic-geometry
at.algebraic-topology
covering-spaces
mixed-hodge-structure
alexander-modules
Compute cohomology of flat fiber bundles - does this always work?
at.algebraic-topology
gt.geometric-topology
fibre-bundles
Are these two notions of "dualizable" spectra equivalent?
at.algebraic-topology
stable-homotopy
Equivalence of Flat Fiber Bundles vs Equivalence of Group Actions on the Fiber
at.algebraic-topology
gn.general-topology
differential-topology
topological-groups
fibre-bundles
Two questions regarding flat fibre bundles and the corresponding group action on the fibre
dg.differential-geometry
at.algebraic-topology
gt.geometric-topology
riemannian-geometry
fibre-bundles
The integral cohomology of real projective space
reference-request
at.algebraic-topology
Topological Complexity $TC$ of two robots moving on number $8$
ag.algebraic-geometry
at.algebraic-topology
graph-theory
homotopy-theory
configuration-spaces
Map between homology of spectra
at.algebraic-topology
stable-homotopy
chromatic-homotopy
Why do polytopes pop up in Lagrange inversion?
co.combinatorics
at.algebraic-topology
convex-polytopes
feynman-integral
ca.classical-analysis-and-odes
Has anyone seen a nice map of multiplicative cohomology theories?
at.algebraic-topology
cohomology
stable-homotopy
ring-spectra
chromatic-homotopy
References for computation of 2-primary stable 64-stem ${_2\pi_{64}^s}$?
reference-request
at.algebraic-topology
What is known about this cohomology operation?
at.algebraic-topology
homotopy-theory
cohomology
What happens if we generalize the fundamental group to make knotted loops distinct?
at.algebraic-topology
knot-theory
Smale's theorem for $C^1$ diffeomorphisms of the sphere
reference-request
dg.differential-geometry
at.algebraic-topology
differential-topology
Relation between de Rham Cohomology group of Lie group as a manifold and group cohomology of Lie group
dg.differential-geometry
at.algebraic-topology
group-cohomology
Lifting local compactness to a covering space
at.algebraic-topology
gn.general-topology
covering
covering-spaces
What is the mistake in the proof of the Homotopy hypothesis by Kapranov and Voevodsky?
at.algebraic-topology
homotopy-theory
higher-category-theory
Fanos with $\chi_{top} = 0$
ag.algebraic-geometry
at.algebraic-topology
Acyclic aspherical spaces with acyclic fundamental groups
at.algebraic-topology
group-cohomology
localization
Are cofibrant commutative S-algebras flat?
at.algebraic-topology
homotopy-theory
model-categories
stable-homotopy
On a Robin Forman's remark on combinatorial simplicial complexes
co.combinatorics
at.algebraic-topology
big-list
simplicial-complexes
formula of b_2 for minimal resolution of surface cyclic quotient singularity
ag.algebraic-geometry
dg.differential-geometry
at.algebraic-topology
Studying the limit of a sequence of spectra knowing their BP-Homology
at.algebraic-topology
stable-homotopy
chromatic-homotopy
Homotopy domination of a wedge of two polyhedra
at.algebraic-topology
homotopy-theory
polyhedra
cw-complexes
Are there geometrically formal manifolds, which are not rationally elliptic?
at.algebraic-topology
gt.geometric-topology
manifolds
rational-homotopy-theory
Equivariant sections of fiber bundles
reference-request
dg.differential-geometry
at.algebraic-topology
differential-topology
fibre-bundles
Fundamental group of the complement homogeneous variety in $\mathbb{C}P^{n-1}$
ag.algebraic-geometry
at.algebraic-topology
complex-geometry
Calculating cup products using cellular cohomology
at.algebraic-topology
cup-product
Jacobian and configuration space and massey products
ag.algebraic-geometry
at.algebraic-topology
rational-homotopy-theory
Compact Lie group action on non-Hausdorff (but CGWH) space with Hausdorff quotient
at.algebraic-topology
gn.general-topology
lie-groups
separation-axioms
pushforward in non-multiplicative generalized cohomology theory
reference-request
at.algebraic-topology
How to show that a spectrum X is not Chromatically Complete
at.algebraic-topology
stable-homotopy
chromatic-homotopy
The Classification of all spaces for which $X$ is a covering space
at.algebraic-topology
covering-spaces
Atiyah duality with coefficients and boundary
at.algebraic-topology
differential-topology
stable-homotopy
manifolds
Is $\Omega J_{p^n-1}S^2$ commutative up to homotopy?
at.algebraic-topology
homotopy-theory
loop-spaces
When does p-profinite completion commutes with maps from a $p$-finite space?
at.algebraic-topology
ct.category-theory
homotopy-theory
profinite-groups
infinity-categories
Whitehead theorem for cohomotopy
at.algebraic-topology
A weak version of the Whitehead Theorems
at.algebraic-topology
homotopy-theory
homology
cw-complexes
Explicit formula for higher order Bockstein
at.algebraic-topology
homological-algebra
Relationship between the cohomology of a group and the cohomology of its associated Lie algebra.
at.algebraic-topology
ra.rings-and-algebras
gr.group-theory
Strong Convergence vs Conditional Convergence for Spectral Sequences (Is there a simple explanation?)
at.algebraic-topology
homological-algebra
spectral-sequences
Continuous map with homeomorphic fibers whose associated $H^{k}_c$ sheaf is not a local system?
at.algebraic-topology
cohomology
sheaf-theory
homology
sheaf-cohomology
Intuition for torsion of a chain complex and application to lens spaces
at.algebraic-topology
gt.geometric-topology
homological-algebra
n-cocycles of finite abelian groups from cohomology group
at.algebraic-topology
finite-groups
group-cohomology
Reference to the theorem about linear bundles
reference-request
at.algebraic-topology
gt.geometric-topology
obstruction-theory
Goeritz matrix and link coloring
at.algebraic-topology
gt.geometric-topology
Differentials in the Adams Spectral Sequence for spheres at the prime p=2
at.algebraic-topology
homotopy-theory
stable-homotopy
spectral-sequences
Stable Dold-Kan correspondence
at.algebraic-topology
homotopy-theory
stable-homotopy
ring-spectra
Must any continuous odd map from $\mathbb{S}^2$ to $\mathbb{R}$ have a path of zeros between antipodal points?
at.algebraic-topology
gn.general-topology
Compactification of open manifolds in the form of a manifold( with zero Euler characteristic)
at.algebraic-topology
gn.general-topology
differential-topology
smooth-manifolds
euler-characteristics
A length decreasing homotopy of a closed curve in a simply connected manifold
dg.differential-geometry
at.algebraic-topology
riemannian-geometry
The fifth k-invariant of BSO(3)
reference-request
at.algebraic-topology
lie-groups
cohomology
Rational cohomology of a contractible $G$-space with finite stabilizers
at.algebraic-topology
cohomology
group-cohomology
What is known about mapping class groups of 4-manifolds?
ag.algebraic-geometry
at.algebraic-topology
gt.geometric-topology
mapping-class-groups
Generalized Classical Adjoints and Factorizations of the Characteristic Polynomial
matrices
linear-algebra
at.algebraic-topology
Realisation of maps between spheres by simplicial maps
at.algebraic-topology
homotopy-theory
simplicial-stuff
simplicial-complexes
free $S^1$ action on $\mathbb{R}P^n$ and $\mathbb{C}P^n$
at.algebraic-topology
gn.general-topology
group-actions
Calculating a certain parameter for an abstract simplicial complex
co.combinatorics
at.algebraic-topology
cohomology
simplicial-complexes
A question about local connectedness in metric spaces
gn.general-topology
at.algebraic-topology
Question regarding the paper by Atiyah, Bott and Shapiro: alternative description of K-theory
at.algebraic-topology
homotopy-theory
vector-bundles
kt.k-theory-and-homology
Does there exist a Haken manifold where all its incompressible surfaces are non-separating?
at.algebraic-topology
gn.general-topology
gt.geometric-topology
differential-topology
hyperbolic-geometry
Combinatorial spin$^{\mathbf{C}}$ structures
co.combinatorics
dg.differential-geometry
at.algebraic-topology
mp.mathematical-physics
Are there any interesting connections between Game Theory and Algebraic Topology?
game-theory
combinatorial-game-theory
at.algebraic-topology
ag.algebraic-geometry
Compute characteristic classes of principal bundle over closed surfaces
dg.differential-geometry
at.algebraic-topology
principal-bundles
Fundamental group of a topological pullback
at.algebraic-topology
Cylinder's triangulation, poset and Foundamental Groups
at.algebraic-topology
Can Bockstein Spectral Sequence detect multiple summands of the same power, in homology?
at.algebraic-topology
homological-algebra
spectral-sequences
Teaching Steenrod Operations
at.algebraic-topology
homotopy-theory
cohomology
simplicial-stuff
teaching
non-simple local coefficient system on a fibration of classifying spaces
at.algebraic-topology
cohomology
spectral-sequences
fibre-bundles
classifying-spaces
a comparison between LS and cohomological dimension
at.algebraic-topology
rational-homotopy-theory
integral or rational cohomology of real grassmannians
at.algebraic-topology
gt.geometric-topology
cohomology
characteristic-classes
grassmannians