Forum / Blog Spotlight – Tori Chic | Forum promotion

Forum / Blog Spotlight

From time to time we will put a forum or blog in the spotlight so that the FP community can get to know new websites or familiarize themselves with existing websites.
Our current spotlight is in a @tori forum

Tori chic

We invite members to visit Tori Chic and become a member if you think the forum suits you.
Use this thread to ask Tori questions about her website or to comment on it.

@tori Please tell us the story of Tori Chic and what is your vision for the site?

Thank you for being part of the forum promotion! .

at.algebraic topology – basic groups of pseudo-Anosov mapping tori

I am trying to create several presentations for the basic set of surface mapping tori.

For example when $ gcd (p, q) = 1 $, then $ M = $ the T.$ (p, q) $ Torus knot outside in $ S ^ 3 $ is a map torus of a genus $ g = frac {pq-p-q + 1} {2} $ Surface with a boundary component, S, which is mapped onto itself $ phi $, a card of order $ pq $.

The suspension flow of this mapping has closed all webs and actually results in a Seifert fiber of $ M $. With the Seifert fiber we can express the basic group quite well in terms of the two singular fibers and the regular fiber. $ pi_1 (M) =$. Here $ z $ is clearly a third-party generator, but is central and includes the class of regular fibers, so somehow nice. The others $ x $ and $ y $ are the classes of the singular order fibers $ q $ and $ p $ respectively.

Since $ M $ is a mapping torus that we also get $ pi_1 (M) = <a_1, …, a_g, b_1, …, b_g, t mathrel {|} ta_it ^ {- 1} = phi _ * (a_i), $ $ tb_it ^ {- 1} = phi _ * (b_i)> = pi_1 (S) rtimes _ { phi_ *} mathbb {Z} $.

The Dehn Twist presentation by $ phi $ is something that can be worked out, and such $ phi _ * $ could actually be specified explicitly.

In order not to go too far, we could instead consider a surface S of the genus $ g geq 2 $ with a boundary component and a pseudo-Anosov monodromy, $ phi $, that gives us a hyperbolic knot outside, M, in $ S ^ 3 $. We get again $ pi_1 (M) = <a_1, …, a_g, b_1, …, b_g, t mathrel {|} ta_it ^ {- 1} = phi _ * (a_i), $ $ tb_it ^ {- 1} = phi _ * (b_i)> = pi_1 (S) rtimes _ { phi_ *} mathbb {Z} $.

Now we have a pseudo-Anosov suspension flow and a collection of closed, singular orbits that correspond to the singularities of the stable and unstable singular leaves. So there should be a representation of the basic group in relation to the closed singular orbits, right?

I'm assuming that I can look at Knot Info's list of hyperbolic node monodromes related to strain rotations to generate examples that I can use to calculate $ phi _ * $ expressly. Then I could fill that out $ ta_it ^ {- 1} = phi _ * (a_i) $ Relators. However, I would like a more general approach since I am interested in all pseudo Anosov monodromes, including narrow surfaces, not just the fiber node monodromy cards in $ S ^ 3 $. Apparently the singular courses are a candidate for a general approach.

I tried to search Thurston's Work on Surfaces (FLP) and I couldn't see such information. Has that been worked out somewhere? If so, then this is probably a reference request. If not, does anyone know of any obstacles to creating the base group with these loops?

Chat! Tori Chic | Forum promotion

Site name: Tori chic

-New content every day!
-Various types of forum games in our game hub!
-Fun job to keep you entertained!
-Weekly newsletter
-User ranks (coming soon)

Hello, the name is Tori. I created Tori Chic forums where people can come and hang out. We have different things for you to do. We want to add games and a reward board. We are just beginning. If you want to take the time, have a look and sign up! We would be very happy.

04/07/2020 – We have reached 27 threads, 50 posts and 6 members!

Hello. I am Tori | Forum promotion

Hey, my name is Tori. I am looking for someone who will work with me over the long term. I want someone who is interested in my forum. Someone who would like to work with me to improve my forum. The forum is just for fun. I want to do more at some point. I want someone to be very interested, willing to help me, make suggestions, work to improve and build a great community.

Thanks for your time.


p adic number theory – conjugation of maximal algebraic tori

Accept $ G $ is a connected, reductive algebraic group over a non-Archimedean local field $ F $which is divided over a finite extent $ E / F $,

I often see a result that says "everything is maximum $ F $-Tori are conjugated over $ E $", by which I understand the following: Let $ G (E) $ denote the $ E $-Dots of the algebraic group $ G $;; then for each maximum $ F $-tori $ T, T $ $ of $ G $is there $ x in G (E) $ so that $ T (E) = xT & # 39; (E) x ^ {- 1} $,

In addition, the definitions show that if $ T, T $ $ are maximum $ F $-tori from $ G $then there is an isomorphism of $ T (F) $ on to $ T & # 39; (F) $ which is defined via $ E $,

My question is: Can the isomorphism be assumed to be conjugation in the second statement (as in the first statement)? That means: it follows from these results that if $ T, T $ $ are maximum $ F $-tori in $ G $then it exists $ x in G (E) $ so that $ T (F) = xT & # 39; (F) x ^ {- 1} $?

Any help (including proof of the first statement) is greatly appreciated!

Abstract algebra – conjugation classes of rational tori in the symplectic group

Rational conjugation classes of Frobenius Stable Tori (in a finite Lie group) are bijected with Frobenius conjugation classes of the corresponding Weyl group$ (2n) $ then the Frobenius action on the Weyl group is trivial and classes of rational Tori are in bijection with conjugation classes of the type C-Weyl group $ W_n $, These conjugation classes are parameterized by bipartitions of n.

The groups of Frobenius stable points of the tori belonging to the conjugation class of the rational tori are all isomorphic. Is there a way to construct these groups from the corresponding bipartite of n? I tried Sp (4), but I can not understand much of what I have. I have also done this calculation for GL (n), for this group this is possible (and quite simple).

I hope someone can give me a hint. Thank you in advance. Hans.

Polyamory Dating UK Asian Free Dating App 2215

Reviewed by Afterbarbag on
Polyamory Dating UK Asian Free Dating App 2215
23 year old woman from 42 years old mankohanka from sitebest friend aususher from modeldating a sagittarius man experiencetransition from relationshipcan internet dating his successfulhookup apps for freereply dating1988 dating100 free dating sites in uaechochschule munich speed dating dating app bio exemplary duel datingearly scan barnsleyhookup or A relationship between a doctor and leading a woman would enable someone who is clinically depressed to determine the speed of dating. Englisch:….php?lang=en. Englisch:….php?lang=en
Rating: 5


ag.algebraic geometry – Are maximal tori conjugated locally localizable?

To let $ S $ to be and leave a scheme $ G to S $ to be a reductive group scheme. Then $ G $ admits that there is a maximal torus etale-local, and two maximal tori are conjugate etale-local, according to Theorem 3.2.6 and Corollary 3.2.7 in [B. Conrad, Reductuve group schemes]

As stated in the book under Proposition 3.1.9 and at the beginning of Chapter 4, the presence of maximum Tori Zariski locally can be achieved (cf. [SGA3, XIV, 3.20]). My question is the following

To let $ T $ and $ T # $ be maximum tori $ G $ over defined $ S $are they conjugated Zariski-local?

In my case, $ T $ is split $ S $, and $ S $ is affine with $ Pic (S) = 0 $,

I would appreciate comments!

ag.algebraic geometry – Tori classes in the Grothendieck variety ring

Inspired by this question, I wondered if it is possible to write down the class of a normative torus $ K_0 ( operatorname {var} _k) $ only use $ mathbb {L} $ and classes of étale algebras. I know it's possible for quasi-split Tori $ R_ {K / k} ( mathbb {G} _m) $by an inclusion-exclusion principle (see this document by Rökaeus), hence for the Formi $ R_ {K / k} ( mathbb {G} _m) / mathbb {G} _m $and the question I ask relates to the duals of it.

I can not say anything in the case $[K:k]= 4 $,

Note: If a torus can be written as a polynomial in $ mathbb {L} $ with coefficients classes of the étalen algebras, then passing on $ l $-adic cohomology become the coefficients $ lambda $– Forces of the character grid of the torus.

A proof that Norm-1-Tori in general can not only be written with $ mathbb {L} $ Even more interesting would be the teaching of étaler algebras.

algebraic groups – maximum tori of a symmetric subgroup

Accept $ G $ is a complex connected reductive algebraic group, $ K $ is a symmetric subgroup of $ G $ (ie the fixed points of an involution $ theta $ from $ G $), and $ T $ is a $ theta $– stable maximum torus in $ G $, Which assumptions do we need? $ G $, $ K $, and $ T $ in order to $ S = K cap T $ is connected and a maximum torus of $ K $?