The Fundamental Group of a Pair of Hawaiian Earrings

This morphism is not surjective, for the exact same reason $pi(H)$ is not the free group with countably many generators.

Just as there are loops in $pi_1(H)$ that go through an infinite sequence of circles,

here you have loops in $pi_1(H cup H')$ that go through an infinite sequence of circles, and who change whose circle they're using an infinite amount of times (for example, just pick the $nth$ circle from the left if $n$ is even, and from the right if $n$ is odd).

So for the same reason, the free product doesn't give you all the cycles, and that morphism is not an isomorphism.However, I'm pretty sure you can find an isomorphism between $pi_1(H cup H')$ and $pi_1(H)$, because they are homeomorphic.

For example, send the circle of radius $1/n$ of the $H$ from $H cup H'$ onto the circle of radius $1/2n$ of $H$ ; and the circle of radius $1/n$ of the $H'$ from $H cup H'$ onto the circle of radius $1/(2n-1)$ of $H$.

• Related Questions

What are cute creative ways to give my girlfriend stud earrings?

I remember seeing someone do this at a restaurant or something...maybe on television but I thought it was adorable. I think they ordered a dessert which was vanilla ice cream and shared it. The man who planned to give the woman jewelry had wrapped the box in a plastic bag and put it in the bowl so the ice cream covered it. And then the woman got to the bottom and so on. Also another idea is writing down a romantic love quote and the place where the box of earrings is hidden. (I think it would be cute if you gave it to her at nighttime so you could go hunting for it in the moonlight) Then cut up the little paper and give it to her in a box for earrings so she thinks she is going to get them easily. When she opens the box she needs to assemble the puzzle and then go find the box of earrrings. I think its very cute. (Hide it in a park or somewhere romantic and maybe to add to it you could have a little picnic or something).


Hard, Crusty Earring Holes?

leave them in, be conscious plenty and plenty alchohol each and every time you think of roughly it. positioned Vaseline on your ears with a sparkling swab. Use a diverse swab for each ear. and do not forget to curve your jewelry so as that they are no longer getting caught on your ear. The brown goo is previous blood. purely shop them sparkling with alcohol and get a sparkling jar of Vaseline. confirm that once you cope with your ears and swabs that your hands are freshly washed! do no longer contaminate your jar of Vaseline via touching the swab on your ear then back into the jar! Germs will start to enhance and additionally you will have a multitude on your hands. The Vaseline will preclude them from getting crusty so the exterior would not harm open. Or call the region the place to procure them pierced and ask them what to do. in the experience that your lobes are crimson and start to ooze eco-friendly fluid, they're contaminated and additionally you probably ought to work out a doctor for antibiotics


Is it okay to bring your own earrings to a piercing parlor?

Its not a matter of a shop being cheap, its a matter of cross contamination. A PROFESSIONAL shop would not allow jewelry from anywhere outside of the shop because they do not know where the jewelry came from, if it was already in someone elses body, or if it is of quality metal. There are only 5 materials that you can get pierced with initially and often times jewelry stores sell cheaply made products. Now that doesn't mean you can't wear your chosen earring after the piercing is fully healed, you just have to start with something a bit basic but of the correct quality. I would bring the earring with you to show the piercer that that is the piece you want to switch it to later, that way he knows on what angle to pierce you helix at. I've been piercing professionally for 6 years and have managed two shops so far in my lifetime and its always been a matter of health issues, never about making an extra $10 Bucks. Hope this helps!.


My managers say I can't wear earrings to work because I'm a guy. It is not in the dress code or any paperwork,?

I'm not sure why the other poster said it's gross and looks wierd. Guys have been wearing earrings for a long time. Earrings are not just for girls. Wonder how she'd react if she was told she couldn't wear pants. The double-standard is alive and well as well as biggotry and ignorance.

On to your problem: Employers have the right to dictate what can and can't be worn. I have a strict dress code where I work but it is stated very clearly. I personally think it's wrong you are being denied. If the girls wear earrings, you should be able to as well. The fact that the paperwork doesn't forbid it means you may have a discrimination case working here. This comes down to a group of managers visiting their social views on you because they don't like it personally.You should consider contacting corporate directly and asking them about it. They will probably support the managers but you'll get them thinking. The last thing any company wants is a claim of discrimination.

Good luck!


Are Cartilage earrings, different from regular earrings that go in your "first holes"?

i might look ahead to sort of four or so months till now you turn your cartilage ring. you may desire to make useful that no longer in basic terms the exterior is healed however the cartilage interior has healed besides till now you pass shifting issues around and aggravating it. the hoop they put in your ear top as quickly as they pierced it substitute into probably made especially to permit for swelling, so wait as long as a risk till now switching it out. Which brings me to the jewelry ought to use fantastically lots any piece of rings that seems sturdy on your ear. in simple terms in simple terms remember to scrub the earring in bactine or hydrogen peroxide till now you utilize it and make useful that this is a sturdy steel like sterling silver or gold, no longer in basic terms nickel or something that'll worsen your dermis. additionally, be sure you sparkling the piercing a minimum of as quickly as an afternoon whilst this is therapeutic. Use bactine...this is the suited stuff for piercings. wish this helps!


What does "hold my earrings mean"?

The noise may seem to come from inside your head or from a distance. It may also be steady, pulsating or intermittent. At times, especially for patients who have had tinnitus in one ear for a long period of time, the noise may be perceived as a song or music. This is known as musical hallucination. The tune is often known to the patient because it is a mind trick where the mind processes the noises as a tune.

What causes the ringing in one ear?

Just like with the ringing in both ears, the problem can be caused by a range of things including exposure to loud music. One ear may be more vulnerable. Additionally, in the case of bacterial infection in one ear, you will experience the ringing solely in the affected ear and not in both. Other possible causes include:

High blood pressure

Increased ear sensitivity to blood flow in the inner ear

Reaction to medication such as antibiotics, aspirin and quinine medications

Head and neck injuries

Acoustic neuroma

Minere's disease

TMJ disorders

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How do you know if your piercing hole has formed completely for dangling earrings?

There's not really a "feeling" that you will feel. they say to wait 6 months before you wear dangley earirngs. I had first take them out at like 4 weeks because i had a soccer game and you can't wear jewlery. I was finee. I had like a choir concert or something at like 8 weeks and i wore dangley earrings. My ears are perfectly fine.. I would said, if you're going to wear those, make sure they're not too heavy. And When you take them out for bed or whatever, but studs back in and wear those the nexy day. They just want to make sure that you're holes from correctly. If you were to wear those all of the time then your hole would be more like a slit then a hole. It's for your own sake. Just switch form whatever you wearback to studs. Wear the studs for a couple days. The dangley earrings and thiner the the studs and your ear will form around the smaller earring. So make sure it is to switch. Hope this helped?


Why was, for they were Ishmaelites considered an explanation for why the Midianites had golden earrings in Judges 8:24?

The answer isn't symbolism - it was that the Ishmaelites were wealthy traders of luxury items (gold, jewels, spices) who would travel to distant lands like Ethiopia and Yemen for their precious cargo. They would ride on camels because it was impossible to cross the hostile desert any other way. It was a dangerous trip, and they were well paid for their efforts. In this passage in Judges, the Ishmaelites wore gold earrings because of their wealth from international trade. Even their camels wore expensive finery -- their collars were decorated with gold too.Another place the Ishmaelites appear is Genesis 39:1, where a caravan of Ishmaelite traders purchase Joseph and sell him as a slave on their way through Egypt.

You can see a similar display of wealth when the queen of Sheba (Ethopia) visited Solomon in 1Kings 10. She too came on a caravan of camels and brought enormous quantities of gold, precious stones and spices. She wasn't an Ishmaelite, but she was coming from the country that was the source of their luxury items. See also Psalm 72:15 and Isaiah 60:6.


Sometimes it hurts when I put in earrings. Could my ears be infected?

If by hurt, you mean like, it pokes you, then... I think I know the problem. You don't wear your earrings often. The piercings will eventually close up... so if you wear earrings after a long time, it might be kinda difficult to put them in. And by too much force, it turns red. And when you take them off it does get kinda crusty. That's normal. Same happened to me. Only one of my ear would kinda hurt. But it's not an infection. Notice, that after the earring finally fits in the piercing, the piercing turns normal. So if you take it off that sec, put it back on, it will go in smoothly. But at the first try, your ear will turn kinda red, and kinda hurt. But if you wear your earrings most of the time, that won't happen. If your not a fan of earrings, try wearing light, small, earrings, so that your piercings won't cover up, and hurt the next time you put in your earrings.

Hope this helps! ^_^

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