# Questions tagged [gt.geometric-topology]

Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

**71**

**12**answers

### Compelling evidence that two basepoints are better than one

**21**

**2**answers

### Uniqueness of compactification of an end of a manifold

**51**

**5**answers

### Torsion in homology or fundamental group of subsets of Euclidean 3-space

**68**

**4**answers

### Independent evidence for the classification of topological 4-manifolds?

**62**

**3**answers

### Can every manifold be given an analytic structure?

**50**

**9**answers

### Fundamental groups of noncompact surfaces

**25**

**5**answers

### Compactification theorem for differentiable manifolds ?

**30**

**1**answer

### Not all manifolds can be triangulated: In which dimensions?

**12**

**2**answers

### Example of Noetherian group (every subgroup is finitely generated) that is not finitely presented

**8**

**1**answer

### Loday's characterization and enumeration of faces of associahedra (Stasheff polytopes)

**25**

**6**answers

### Failure of smoothing theory for topological 4-manifolds

**24**

**2**answers

### Are non-PL manifolds CW-complexes?

**26**

**4**answers

### Can all n-manifolds be obtained by gluing finitely many blocks?

**20**

**3**answers

### Cohomology of fibrations over the circle: how to compute the ring structure?

**18**

**3**answers

### What is Kirillov's method good for?

**17**

**6**answers

### Diffeomorphism of 3-manifolds

**12**

**5**answers

### Which manifolds admit a diffeomorphism of order $n$?

**12**

**3**answers

### Linking topological spheres

**9**

**3**answers

### Homeomorphic but Non-Conjugate Mapping Tori

**6**

**2**answers

### G-spaces and manifolds

**10**

**1**answer

### CAT(0) groups that does not act on CAT(0) cubical complex

**52**

**8**answers

### Questions about analogy between Spec Z and 3-manifolds

**54**

**7**answers

### Status of PL topology

**57**

**10**answers

### Nice proof of the Jordan curve theorem?

**50**

**7**answers

### What are the open subsets of $\mathbb{R}^n$ that are diffeomorphic to $\mathbb{R}^n$

**46**

**4**answers

### To which extent can one recover a manifold from its group of homeomorphisms

**30**

**4**answers

### How to visualize the Riemann-Roch theorem from complex analysis or geometric topology considerations?

**18**

**7**answers

### CW-structures and Morse functions: a reference request

**77**

**1**answer

### Topological cobordisms between smooth manifolds

**16**

**3**answers

### When does the tangent bundle of a manifold admit a flat connection?

**51**

**4**answers

### Unusual symmetries of the Cayley-Menger determinant for the volume of tetrahedra

**46**

**3**answers

### Thurston's 24 questions: All settled?

**26**

**3**answers

### finite generated group realized as fundamental group of manifolds

**23**

**3**answers

### Complete knot invariant?

**20**

**1**answer

### connectivity of the group of orientation-preserving homeomorphisms of the sphere

**32**

**1**answer

### Strong Whitney embedding theorem for non-compact manifolds

**29**

**1**answer

### Nilpotence of the stable Hopf map via framed cobordism

**16**

**3**answers

### When are (finite) simplicial complexes (smooth) manifolds?

**31**

**3**answers

### Why are there no wild arcs in the plane?

**22**

**5**answers

### Proof of the Reidemeister theorem

**31**

**1**answer

### Classifiying sphere eversions

**26**

**1**answer

### Fake versus Exotic

**22**

**0**answers

### Monoid structure of oriented manifolds with connect sum

**15**

**3**answers

### Is it true that all sphere bundles are boundaries of disk bundles?

**10**

**1**answer

### Seiberg-Witten theory on 4-manifolds with boundary

**20**

**2**answers

### Manifolds with homeomorphic interiors

**21**

**1**answer

### Word problem for fundamental group of submanifolds of the 4-sphere

**26**

**5**answers

### Complexity of random knot with vertices on sphere

**23**

**1**answer

### Building a genus-$n$ torus from cubes

**15**

**10**answers