# 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).

**211**

**29**answers

### Intuitive crutches for higher dimensional thinking

**124**

**2**answers

### What are the shapes of rational functions?

**105**

**3**answers

### The number $\pi$ and summation by $SL(2,\mathbb Z)$

**90**

**4**answers

### Which manifolds are homeomorphic to simplicial complexes?

**84**

**1**answer

### The mathematical theory of Feynman integrals

**77**

**1**answer

### Topological cobordisms between smooth manifolds

**73**

**3**answers

### Gromov's list of 7 constructions in differential topology

**72**

**5**answers

### When the automorphism group of an object determines the object

**71**

**12**answers

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

**68**

**4**answers

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

**62**

**3**answers

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

**61**

**3**answers

### The story about Milnor proving the Fáry-Milnor theorem

**59**

**2**answers

### The topological analog of flatness?

**58**

**14**answers

### What are some of the big open problems in 3-manifold theory?

**58**

**4**answers

### Tying knots with reflecting lightrays

**57**

**28**answers

### Proofs where higher dimension or cardinality actually enabled much simpler proof?

**57**

**10**answers

### Nice proof of the Jordan curve theorem?

**54**

**7**answers

### Status of PL topology

**52**

**6**answers

### Poincaré Conjecture and the Shape of the Universe

**52**

**8**answers

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

**52**

**3**answers

### Kirby calculus and local moves

**51**

**4**answers

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

**51**

**5**answers

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

**51**

**2**answers

### How to add essentially new knots to the universe?

**51**

**1**answer

### Open map D⁴ → S²

**50**

**7**answers

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

**50**

**9**answers

### Fundamental groups of noncompact surfaces

**50**

**4**answers

### Drawing of the eight Thurston geometries?

**48**

**2**answers

### Can knot diagrams be monotonically simplified using under moves?

**47**

**3**answers

### Explicit metrics

**46**

**3**answers

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

**46**

**4**answers

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

**41**

**8**answers

### Classification problem for non-compact manifolds

**41**

**4**answers

### Elegant proof that any closed, oriented 3-manifold is the boundary of some oriented 4-manifold?

**41**

**7**answers

### Why should I care about Heegaard-Floer theory?

**40**

**1**answer

### Pach's “Animals”: What if the genus is positive?

**39**

**6**answers

### Triangulating surfaces

**39**

**1**answer

### Four circles on the sphere

**39**

**0**answers

### Minimal volume of 4-manifolds

**38**

**5**answers

### Can cotangent bundles see exotic smooth structures?

**38**

**2**answers

### Meaning/Origin of Seiberg-Witten Equations/Invariants

**38**

**0**answers

### Homotopy type of TOP(4)/PL(4)

**37**

**9**answers

### In knot theory: Benefits of working in $S^3$ instead of $\mathbb{R}^3$?

**37**

**9**answers

### Applications of knot theory

**37**

**4**answers

### Thurston's “tinker toy” problem

**37**

**1**answer

### Exotic $R^4$ as the universal covering space

**37**

**2**answers

### Knot security (When to trust your life with a knot)

**36**

**3**answers

### Does Euclidean space have a compact factor?

**36**

**1**answer

### Are there only countably many compact topological manifolds?

**36**

**2**answers