# 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).

**4**

**3**answers

### About the proof of Wajnryb's finite presentation of Mod(S)

**19**

**0**answers

### Polynomials with roots in convex position

**18**

**4**answers

### Free splittings of one-relator groups

**12**

**2**answers

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

**211**

**29**answers

### Intuitive crutches for higher dimensional thinking

**8**

**1**answer

### Does every retraction of free groups arise from projection to a subset of a freely generating set?

**8**

**2**answers

### Can we make rigorous the 'obvious' characterisation of singular homology?

**7**

**2**answers

### tangent sphere bundle over sphere

**5**

**1**answer

### Do continuous maps give continuity in the 'topology' of Hausdorff distance?

**8**

**2**answers

### limiting behaviour of converging loops on a torus

**7**

**4**answers

### Do you know how to construct a compact hyperbolic 3-manifold with three or four totally geodesic boundary components?

**4**

**2**answers

### Properties of the n-dimensional Stereographic Projection

**27**

**2**answers

### Does every finitely presentable group have a presentation that simultaneously minimizes the number of generators and number of relators?

**7**

**1**answer

### Counting submanifolds of the plane

**86**

**1**answer

### The mathematical theory of Feynman integrals

**50**

**4**answers

### Drawing of the eight Thurston geometries?

**17**

**1**answer

### Locus of equal area hyperbolic triangles

**5**

**2**answers

### Is there a knotted torus in 4-sphere whose complement's fundamental group is infinite cyclic ?

**5**

**3**answers

### How big can the Hausdorff dimension of a function graph get?

**5**

**1**answer

### Automorphisms of $\pi_1$ induced by pseudo-Anosov maps

**9**

**3**answers

### A Reference for Schubert's Theorem

**21**

**2**answers

### Does this approach for the Poincaré conjecture work?

**9**

**5**answers

### Möbius and projective 3-manifolds

**16**

**2**answers

### The kernel of the map from the handlebody group to Outer automorphisms of a free group

**2**

**2**answers

### Group action, Fixed point set and Orbit Space

**10**

**3**answers

### Is every (finite) group action on R^n by diffeomorphisms conjugate to a linear action?

**10**

**1**answer

### Self-homomorphisms of surface groups

**25**

**5**answers

### Compactification theorem for differentiable manifolds ?

**5**

**2**answers

### Classification of mapping tori

**13**

**2**answers

### exotic differentiable structures on manifolds in dimensions 5 and 6

**5**

**2**answers

### A question about axes of symmetry in the plane.

**12**

**3**answers

### To what extent is convexity a local property?

**11**

**2**answers

### Isometry classification of spherical space forms

**18**

**2**answers

### Turning pants inside-out (or backwards) while tied together

**7**

**2**answers

### Knot complement diffeomorphism groups and embedding spaces

**6**

**1**answer

### Rational homotopy type of a complement

**4**

**1**answer

### Contractability of Exotic R^4s

**6**

**1**answer

### Weight filtration for smooth analytic manifolds

**3**

**1**answer

### How to shown that the Tangent Bundle of a vector space is a Vector Bundle

**9**

**1**answer

### Applications of Faber's conjecture

**11**

**1**answer

### classification of smooth involutions of torus

**2**

**1**answer

### isotropic deformation retract of Weinstein manifolds?

**5**

**1**answer

### Heegaard genus in hyperbolic 3-manifolds

**13**

**3**answers

### Rational homotopy theory of a punctured manifold

**17**

**2**answers

### Involutions of $S^2$

**3**

**1**answer

### Singular, holonomy-free connections on Riemannian surfaces?

**18**

**4**answers

### Why is complex projective space triangulable?

**15**

**10**answers

### Orbifold fundamental group in terms of loops?

**10**

**2**answers

### Presentation of the monoid of surfaces

**39**

**0**answers