Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with knot-theory
Search options not deleted
user 4707
Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.
8
votes
1
answer
305
views
What does the representation category of the knot group know?
Let $K, K'$ be knots in $S^3$, and $T, T'$ the boundaries of their tubular neighborhoods.
Recall that by theorems of Waldhausen, and Gordon and Luecke, one knows the following: an isomorphism $[\pi_ …
- 8,723
-1
votes
Accepted
What does the representation category of the knot group know?
So long as I allow myself infinite size representations, and writing $\mathbb{Z}[G]-mod$ for representations of $G$ in $\mathbb{Z}$-modules, then so long as I have the forgetful functor
$$\mathbb{Z}[ …
- 8,723
4
votes
1
answer
321
views
{0,1} Maslov potentials on Legendrian knots
A Legendrian knot is a curve in $\mathbb{R}^3$ on which $dz - ydx$ vanishes identically. Its projection to the $x,z$ plane is called a front diagram; as we can recover $y = dz/dx$ this determines the …
- 8,723
11
votes
3
answers
2k
views
When do two positive braids represent the same link?
Let $B_n$ be the braid group on $n$ strands, with the usual generators: $s_1, \ldots, s_{n-1}$ and their inverses, where $s_i$ is a positive half-twist interchanging the strands labelled $i$ and $i+1$ …
- 8,723
1
vote
Genera and the Milnor Conjecture on the Unknotting Number of a Torus Knot
It is a bit unclear what you are asking. The thing you call the geometric genus is certainly not the geometric genus; the literal object you wrote is $\infty$ and if you first compactified the curve …
- 8,723
13
votes
1
answer
765
views
Are homological knot invariants of finite type?
It is well known that, after a change of variables, the quantum knot invariants (Jones, HOMFLY, Kauffman, etc.) can be written as power series whose coefficients are finite type (i.e., Vassiliev) inva …
- 8,723
6
votes
1
answer
629
views
What is the image of the half/full twist in the Hecke algebra, in the Kazhdan-Lusztig basis?...
Let $B_n$ be the braid group on $n$ strands. It has generators $\tau_i$ for $i = 1,\ldots,n-1$ which exchange the $i$th and $(i+1)$st strands, and which satisfy the relations
$\tau_i \tau_j = \tau_j …
- 8,723
4
votes
0
answers
609
views
Positivity of braid monodromy of curve singularities
I recall the notion of braid monodromy. Let $C \subset \mathbb{C}^2$ be an algebraic curve, and choose a projection $\pi: \mathbb{C}^2 \to \mathbb{C}$ such that the restriction $\pi: C \to \mathbb{C …
- 8,723
12
votes
0
answers
385
views
The Markov trace via Bott-Samelson fibers?
Let $H_n$ be the Hecke algebra of GL(n), i.e., the algebra over $\mathbb{Q}(q)$ with generators $T_1,
\ldots, T_{n-1}$ which satisfy the braid relations and also $T^2 = (q-1) T + q$.
Recall the Mar …
- 8,723