# 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).

**20**

**3**answers

### What is the geometric shape of the Monster sporadic group?

**5**

**1**answer

### Hyperbolic manifolds with infinite cyclic fundamental group

**4**

**2**answers

### How to compute fundamental groups of closed surfaces without using Van-Kampen theorem?

**2**

**1**answer

### Does tangle closure determine the triviality of the tangle?

**7**

**0**answers

### Are triangulations of n-dimensional manifolds determined by lower-dimensional skeleta?

**19**

**1**answer

### Can every manifold be dominated by a parallelizable one?

**11**

**1**answer

### Does there exist a non-zero signed finite borel measure which is zero on all balls?

**5**

**0**answers

### $\mathbb{Z}/2\mathbb{Z}$ coefficients in gysin sequence

**3**

**2**answers

### On what proper Gromov hyperbolic space does a free product act?

**7**

**1**answer

### Understanding fundamental group of Poincare homology sphere

**4**

**0**answers

### Controlling the intersection of two surfaces in $\mathbb{R}^3$

**7**

**1**answer

### Thickness and hierarchical hyperbolicity

**4**

**0**answers

### Smoothability of open 4-manifolds

**1**

**0**answers

### Boundary map for Mayer-Vietoris sequence for Bordism

**10**

**1**answer

### Free product decompositions of the fundamental group of Hawaiian Earrings

**2**

**0**answers

### Full automorphism group of a Bruhat-Tits building

**3**

**0**answers

### Approximative extension of the autohomeomorphism of the complement of the trivial knot?

**7**

**1**answer

### Resolution graphs in the sense of Némethi

**4**

**0**answers

### Contractibility and orientation double cover

**5**

**0**answers

### Lattices of minimal covolume in $\operatorname{SL}_2(\mathbb{R}) \times \operatorname{SL}_2(\mathbb{R})$

**4**

**2**answers

### Finite models for torsion-free lattices

**5**

**1**answer

### 3-balls with the same boundary in $S^4$ differ up to diffeomorphism

**4**

**0**answers

### program to compute hurwitz numbers

**12**

**2**answers

### Cobordism and Kirby calculus

**8**

**2**answers

### On Gromov's proof of the systolic inequality $\operatorname{Sys}_1(M)\leq 6\operatorname{FillRad}(M)$

**1**

**2**answers

### Non-self-intersecting paths on $\mathbb{C}\setminus\{0,1\}$ [closed]

**10**

**1**answer

### Kirby calculus on Mazur manifolds

**11**

**2**answers

### Acyclic group and finite CW-complex

**5**

**1**answer

### Lengths of closed geodesics on a flat vs hyperbolic punctured torus

**1**

**0**answers

### Conjugation map on $\mathbb CP^n\smallsetminus \mathring{D}^{2n}$ that preserves boundary, $n\geq 4$ even

**2**

**1**answer

### The isometric immersion of a positively curved projective plane in 3-dimensional Euclidean space?

**3**

**1**answer

### The plumbing graphs of Brieskorn spheres

**5**

**1**answer

### Applications of quantum representations of the mapping class group to quantum computers

**2**

**2**answers

### Alexander duality and homology equivalence

**8**

**3**answers

### Heegaard splittings of Brieskorn spheres

**4**

**0**answers

### An upper bound for second type of Reidemeister move

**5**

**1**answer

### Multisignature and homeomorphism type

**0**

**0**answers

### Smooth immersed surfaces with an unknot as the boundary in $S^3$

**12**

**1**answer

### Classifying space for Thompson's group F?

**9**

**2**answers

### Existence of fibered surfaces in arbitrary 4-manifolds?

**8**

**0**answers

### Dualizing module for $\operatorname{Aut}(F_n)$

**3**

**1**answer

### Topology on the boundary compactification $X^{-}=\partial X\cup X$ of a Gromov-hyperbolic space

**7**

**0**answers

### Self diffeomorphism of $S^2\times S^2$

**8**

**1**answer

### Topological mapping class groups of 4-manifolds

**7**

**0**answers

### Long non-deformable hyperbolic fillings

**3**

**0**answers

### Hochschild cohomology of (generalizations) of Khovanov's arc algebra

**14**

**0**answers

### Hauptvermutung for non-manifolds

**9**

**0**answers

### Finite quotients of surface braid groups

**9**

**2**answers

### A plausible hyperbolic link

**3**

**1**answer