Unsolved Problems
Showing 1-5 of 5 problems
Rank vs. Genus
Question Is there a hyperbolic 3-manifold whose fundamental group rank is strictly less than its Heegaard genus? How much can the two differ by?...
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?
Problem Determine a computable set of invariants that allow one to determine, given a compact boundaryless 3-manifold, whether or not it embeds smooth...
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?
Problem Is there an algorithm which takes as input a triangulated 4-manifold, and determines whether or not this manifold is combinatorially equivalen...
Unsolvability of word problem for 2-knot complements
Problem Does there exist a smooth/PL embedding of $S^2$ in $S^4$ such that the fundamental group of the complement has an unsolvable word problem?...
Several ways to apply a (multivalued) multiargument function to a family of filters
Problem Let $\mathcal{X}$ be an indexed family of filters on sets. Which of the below items are always pairwise equal? 1. The funcoid corresponding t...