悢妛摿榑7

扨懱揑暋懱偺杽傔崬傒

島媊奣梫丗
偙偺庼嬈偱偼丄僩億儘僕乕偺堦暘栰偱偁傞乽扨懱揑暋懱偲偦偺杽傔崬傒棟榑乿傪埖偄傑偡丅嬶懱揑偵偼丄扨懱揑暋懱偺婎慴揑側掕媊偐傜巒傑傝丄杽傔崬傒壜擻惈偺敾掕丄儂儌儘僕乕棟榑偺墳梡丄僋儔僩僼僗僉乕偺掕棟傗椪奅揑暋懱偺峔憿偵偮偄偰妛傃傑偡丅傑偨丄3師尦媴柺傗儐乕僋儕僢僪嬻娫傊偺杽傔崬傒偺婔壗妛揑惈幙傗惂栺傪媍榑偟丄杽傔崬傒棟榑偺尰戙揑側尋媶壽戣偵怗傟傞偙偲偱丄棟榑偲墳梡偺椉柺偐傜棟夝傪怺傔傑偡丅嵟廔揑偵丄杽傔崬傒棟榑偺僩僺僢僋傪摑崌揑偵棟夝偟丄娭楢偡傞悢妛揑側媍榑傪峴偊傞傛偆偵側傞偙偲傪栚巜偟傑偡丅
庼嬈偺摓払栚昗丗
1. 扨懱揑暋懱偲杽傔崬傒偺婎杮揑側掕媊偲惈幙傪棟夝偡傞
丒扨懱丄暋懱丄廳怱嵶暘丄杽傔崬傒側偳偺婎杮奣擮傪惓妋偵愢柧偱偒傞丅
丒僕儑儖僟儞嬋慄掕棟傗僋儔僩僼僗僉乕偺掕棟傪棟夝偟丄偦傟傜傪揔梡偱偒傞丅
2. 扨懱揑暋懱偺杽傔崬傒壜擻惈偺棟榑傪廗摼偡傞
丒扨懱揑暋懱偑摿掕偺嬻娫偵杽傔崬傔傞忦審傪敾掕偡傞偨傔偺婎杮揑側庤朄傪廗摼偡傞丅
丒儐乕僋儕僢僪嬻娫傊偺杽傔崬傒壜擻惈傗偦偺惂栺偵偮偄偰媍榑偱偒傞丅
3. 杽傔崬傒偲儂儌儘僕乕棟榑偺娭學傪棟夝偡傞
丒扨懱揑暋懱偺儂儌儘僕乕孮偺寁嶼偑杽傔崬傒壜擻惈傗婔壗妛揑峔憿偺棟夝偵偳偺傛偆偵栶棫偮偐傪愢柧偱偒傞丅
4. 椪奅揑暋懱傗懡廳暘婒嬋柺偺惈幙傪暘愅偱偒傞
丒椪奅揑側暋懱傗惓懃懡廳暘婒嬋柺偵娭楢偡傞尰戙揑側尋媶壽戣偵偮偄偰媍榑偱偒傞丅
丒偙傟傜偺峔憿偑偳偺傛偆偵杽傔崬傒棟榑偵塭嬁傪梌偊傞偐傪棟夝偡傞丅
5. 杽傔崬傒棟榑偺奣擮傪梡偄偰撈帺偺媍榑傪揥奐偱偒傞
丒妛傫偩撪梕傪婎偵丄怴偟偄栤戣愝掕傗墳梡椺傪峫嶡偟丄娙寜偐偮榑棟揑偵愢柧偱偒傞丅
帠慜丒帠屻妛廗偺撪梕丗
帠慜妛廗: 奺夞偺僥乕儅偵増偭偰嫵壢彂傪撉傒丄掕媊傗婎杮揑側椺傪棟夝偡傞丅摿偵廳梫側掕棟傗惈幙偵偮偄偰偼丄偦偺攚宨傗揔梡椺傪挷嵏偟丄梊廗栤戣傪夝偔偙偲偱婎慴傪屌傔傞丅
帠屻妛廗: 庼嬈撪梕傪惍棟偟丄庼嬈拞偺椺戣傪暅廗偡傞丅怴偟偄栤戣傪夝偄偰棟夝傪怺傔丄娭楢偡傞掕棟傗庤朄傪懠偺嬶懱椺偵揔梡偟偰墳梡椡傪梴偆丅傑偨丄嫵壢彂傗嶲峫暥專傪梡偄偰晄懌晹暘傪曗嫮偡傞丅
庼嬈寁夋丗
  1. 戞1夞丗摫擖 - 杽傔崬傒偺婎慴
    杽傔崬傒偺掕媊偲椺丅僕儑儖僟儞嬋慄掕棟丅僕儑儖僟儞-僽儔僂傾乕偺暘棧掕棟丄僕儑儖僟儞-僔僃乕儞僼儕乕僗偺掕棟偲傾儗僋僒儞僟乕偺妏晅偒媴柺丅
    嶲峫暥專丗James R. Munkres, Topology丄Allen Hatcher, Algebraic Topology丄彫戲 惤, 傾儗僋僒儞僟乕偺妏晅偒媴柺, 悢妛僙儈僫乕 2019擭11寧崋
  2. 戞2夞丗扨懱揑暋懱偺掕媊
    扨懱丄暋懱偲懡柺懱丄廳怱嵶暘丄扨懱暘妱丄扨懱幨憸偲嬫暘慄宍幨憸丄扨懱嬤帡掕棟丅
    嶲峫暥專丗揷懞堦榊, 僩億儘僕乕丄怷尦姩帯, 3師尦懡條懱擖栧
  3. 戞3夞丗僋儔僩僼僗僉乕偺掕棟
    暯柺揑僌儔僼丄僆僀儔乕昗悢丄僼傽儞丒僇儞儁儞忈奞擖栧
    嶲峫暥專丗Adrian Bondy, U.S.R. Murty, Graph Theory丄Arkadiy Skopenkov, Embedding and knotting of manifolds in Euclidean spaces, arXiv:math/0604045
  4. 戞4夞丗僋儔僩僼僗僉乕偺掕棟偺徹柧
    2-楢寢僌儔僼偲僒僀僋儖丄僋儔僩僼僗僉乕偺掕棟偺徹柧
    嶲峫暥專丗Adrian Bondy, U.S.R. Murty, Graph Theory丄Mary Radcliffe, Math 228: Kuratowski乫s Theorem
  5. 戞5夞丗儐乕僋儕僢僪嬻娫傊偺杽傔崬傒壜擻惈
    堦斒偺埵抲偺掕棟丄扨懱揑暋懱偺儐乕僋儕僢僪嬻娫傊偺杽傔崬傒壜擻惈偲晄壜擻惈
    嶲峫暥專丗John Stillwell, Classical Topology and Combinatorial Group Theory丄Francis Lazarus, Embedding in Euclidean spaces: the double dimension case
  6. 戞6夞丗儂儌儘僕乕孮偺掕媊
    扨懱揑暋懱丄儂儌儘僕乕孮偺掕媊丄僆僀儔乕昗悢偲儀僢僠悢偺娭學
    嶲峫暥專丗揷懞堦榊, 僩億儘僕乕丄James R. Munkres, Elements of Algebraic Topology
  7. 戞7夞丗杽傔崬傑傟偨晹暘懡條懱偺儂儌儘僕乕
    儅僀儎乕丒償傿乕僩儕僗姰慡宯楍丄暵嬋柺偺儂儌儘僕乕孮丄3師尦媴柺偺晹暘懡條懱偺儂儌儘僕乕孮
    嶲峫暥專丗揷懞堦榊, 僩億儘僕乕丄James R. Munkres, Elements of Algebraic Topology
  8. 戞8夞丗椪奅揑側懡廳暘婒嬋柺
    懡廳暘婒嬋柺偺掕媊丄3師尦媴柺偵娭偟偰椪奅揑側懡廳暘婒嬋柺偺儕僗僩
    嶲峫暥專丗Kazufumi Eto, Shosaku Matsuzaki, Makoto Ozawa, An obstruction to embedding 2-dimensional complexes into the 3-sphere丄Shosaku Matsuzaki, Makoto Ozawa, Genera and minors of multibranched surfaces
  9. 戞9夞丗惓懃懡廳暘婒嬋柺偺庬悢
    惓懃懡廳暘婒嬋柺偺掕媊丄僸乕僈乕僪庬悢丄惓懃懡廳暘婒嬋柺偺庬悢偺昡壙幃
    嶲峫暥專丗Kazufumi Eto, Shosaku Matsuzaki, Makoto Ozawa, An obstruction to embedding 2-dimensional complexes into the 3-sphere丄Shosaku Matsuzaki, Makoto Ozawa, Genera and minors of multibranched surfaces
  10. 戞10夞丗惓懃懡廳暘婒嬋柺偺嵟戝丒嵟彫庬悢
    嵟戝庬悢偲嵟彫庬悢偺掕媊偲昡壙幃
    嶲峫暥專丗Mario Eudave-Munoz, Makoto Ozawa, The maximum and minimum genus of a multibranched surface
  11. 戞11夞丗僌儔僼偲墌廃偺捈愊
    僋儔僩僼僗僉乕僌儔僼偲墌廃偺捈愊偐傜摼傜傟傞椪奅揑暋懱丄僌儔僼偲墌廃偺捈愊傪2師尦晹暘偵帩偮椪奅揑扨懱揑暋懱偺摿挜晅偗
    嶲峫暥專丗Mario Eudave-Munoz, Makoto Ozawa, Forbidden complexes for the 3-sphere
  12. 戞12夞丗杽傔崬傒偺摨抣娭學
    扨懱揑暋懱娫偺杽傔崬傒偵傛傞摨抣娭學丄杽傔崬傒偵傛傞敿弴彉廤崌偺惈幙
    嶲峫暥專丗Mario Eudave-Munoz, Makoto Ozawa, Forbidden complexes for the 3-sphere
  13. 戞13夞丗椪奅揑暋懱
    僋儔僩僼僗僉乕僌儔僼忋偺悕丄嫬奅傪帩偮椪奅揑暋懱丄椪奅揑旕惓懃扨懱揑暋懱
    嶲峫暥專丗Mario Eudave-Munoz, Makoto Ozawa, Forbidden complexes for the 3-sphere丄Makoto Ozawa, Current list of forbidden complexes for the 3-sphere
  14. 戞14夞丗婜枛僥僗僩
    偙傟傑偱妛傫偩偙偲偵偮偄偰僥僗僩偟傑偡丅
嫵壢彂丗
亀扨懱揑暋懱偺杽傔崬傒亁彫戲惤
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