M surface compact with a point removed, genus g has the same homotopy type as 2g circles

up vote
0
down vote

favorite

Let $M$ be a compact orientable surface of genus $g$. Let $pin M$ Prove that $Msetminusleftpright$ has the same homotopy type as $2g$ circles with a point in common."

I have not idea proves this exercise.
I only have the intuition that appears on the image on page 5 of the hatcher's book. http://pi.math.cornell.edu/~hatcher/AT/AT.pdf

edited Sep 2 at 5:13

asked Sep 2 at 5:05

eraldcoil

468

add a commentÂ |Â

up vote
0
down vote

favorite

Let $M$ be a compact orientable surface of genus $g$. Let $pin M$ Prove that $Msetminusleftpright$ has the same homotopy type as $2g$ circles with a point in common."

I have not idea proves this exercise.
I only have the intuition that appears on the image on page 5 of the hatcher's book. http://pi.math.cornell.edu/~hatcher/AT/AT.pdf

edited Sep 2 at 5:13

asked Sep 2 at 5:05

eraldcoil

468

add a commentÂ |Â

up vote
0
down vote

favorite

Let $M$ be a compact orientable surface of genus $g$. Let $pin M$ Prove that $Msetminusleftpright$ has the same homotopy type as $2g$ circles with a point in common."

I have not idea proves this exercise.
I only have the intuition that appears on the image on page 5 of the hatcher's book. http://pi.math.cornell.edu/~hatcher/AT/AT.pdf

edited Sep 2 at 5:13

asked Sep 2 at 5:05

eraldcoil

468

Let $M$ be a compact orientable surface of genus $g$. Let $pin M$ Prove that $Msetminusleftpright$ has the same homotopy type as $2g$ circles with a point in common."

I have not idea proves this exercise.
I only have the intuition that appears on the image on page 5 of the hatcher's book. http://pi.math.cornell.edu/~hatcher/AT/AT.pdf

homotopy-theory

edited Sep 2 at 5:13

asked Sep 2 at 5:05

eraldcoil

468

edited Sep 2 at 5:13

asked Sep 2 at 5:05

eraldcoil

468

edited Sep 2 at 5:13

asked Sep 2 at 5:05

eraldcoil

468

asked Sep 2 at 5:05

eraldcoil

468

asked Sep 2 at 5:05

eraldcoil

468

add a commentÂ |Â

active

oldest

votes

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\$","\$"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);

);

draft saved

draft discarded

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2902360%2fm-surface-compact-with-a-point-removed-genus-g-has-the-same-homotopy-type-as-2g%23new-answer', 'question_page');

);

Post as a guest

Name

active

oldest

votes

draft saved

draft discarded

draft saved

draft discarded

Post as a guest

Name

搜尋此網誌

Vtyjkyuk