Search Results

For Question 2: In addition to Kellerhals' lower bounds on $\epsilon(n)$, there is an absolute constant $C>0$ such that $$ \epsilon(n)\le \frac{C}{\sqrt{n}}, $$ see Proposition 5.2 in Belolipetsky, Mi …

If you read our paper a bit further, you will find that on page 348 we mention that this result is due to Eberlein and give a reference to his 1982 paper. More precisely, he proves a more general theo …

You seem to be asking two different questions: The first question appears to be: "Given a family of closed geodesics ${\mathcal F}$ which exits an end $E$, is it true that there are members of ${\ma …

First of all, fundamental groups of compact hyperbolizable 3-manifolds (with or without boundary) are LERF, this is one corollary of the work by Agol, Haglund and Wise. The LERF property is unaffecte …

This is a direct corollary of Federer -Flemming deformation Lemma saying that vary small area sphere can be homotoped to 1-skeleton of the fixed triangulation of the manifold. The dimension assumption …

As stated, your question is rather hopeless. Consider the 3-sphere, which also happens to admit the Hopf fibration over the 2-sphere. Then classifying 2-tori in the 3-sphere is essentially equivalent …

Since every homotopy class of loops is represented by infinitely many knots, the only way I can interpret the question is: Is there a characterization of commuting pairs of elements $\alpha, \beta$ o …

The long exact sequence of the pair $(M, \partial M)$ combined with Poincare duality immediately imply that the natural map $$ i_*: H_1(\partial M)\to H_1(M) $$ cannot be an isomorphism, unless $H_1 …

Just use the suspension flow of the periodic diffeomorphism $f: S\to S$ in the periodic mapping class. Then all flow lines will be periodic (i.e., circles) and you are done; the base will be the quoti …

Here is the detailed answer. First, you have to assume that your hyperbolic manifold is complete and has finitely generated fundamental group, otherwise you will get no answer except for the tautologi …

There is actually an old (ca 1986) example of nonreduced $SL(2, {\mathbb C})$-representation scheme of a 3-manifold group. Take an oriented Seifert manifold $M$ which fibers over the $S^2(3,3,3)$ orbi …

I assume that you want $P$ to be a fundamental domain for $G$. Then the answer is positive, see: I. Kapovich, R. Weidmann, Kleinian groups and the rank problem. Geom. Topol. 9 (2005), 375-402.