悢妛摿榑7

寢傃栚棟榑偺枹夝寛栤戣侾侽

島媊奣梫丗

埵憡婔壗妛乮僩億儘僕乕乯偼埵抲乮亖埵乯偲宍乮亖憡乯傪埖偆婔壗妛偱偡丅 宍偼懡條懱榑偲偟偰丄埵抲偼寢傃栚棟榑偲偟偰尋媶偝傟偰偄傑偡丅 偙偺庼嬈偱偼丄寢傃栚棟榑偺10屄偺枹夝寛栤戣偵偮偄偰夝愢偟傑偡丅

庼嬈偺摓払栚昗丗

悢妛偺愱栧暘栰偵偍偄偰丄偳偺傛偆側栤戣偑偁傞偺偐傪抦傝丄傑偨偦偺撪梕傪棟夝偡傞偙偲偼擄偟偄丅 偙偺庼嬈偱偼丄寢傃栚棟榑偱偳偺傛偆側栤戣偑偁傝丄傑偨偦偺撪梕傪棟夝偡傞堊偺抦幆傪廗摼偡傞偙偲傪栚昗偲偡傞丅

帠慜丒帠屻妛廗偺撪梕丗

梊旛抦幆偲偟偰偼埵憡嬻娫乮摨憡幨憸摍乯傪壖掕偡傞丅

庼嬈寁夋丗

1. 戞侾夞丂寢傃栚偲懡條懱 寢傃栚偺掕媊偲摨抣娭學偵偮偄偰妛傃傑偡丅傑偨丄娭楢偡傞3師尦懡條懱偵偮偄偰妛傃傑偡丅
2. 戞俀夞丂寢傃栚偺晄曄検 寢傃栚偺岎揰悢丄夝徚悢丄嫶悢丄僽儗僀僪巜悢丄暆丄僩儔儞僋偵偮偄偰妛傃傑偡丅
3. 戞俁夞丂寢傃栚偺婎慴抦幆 寢傃栚偺嫬奅僗儘乕僾丄杮幙揑嬋柺丄憃嬋懱愊丄僨乕儞庤弍偵偮偄偰妛傃傑偡丅
4. 戞係夞丂Additivity problem 寢傃栚偺楢寢榓偵娭偟偰晄曄検乮岎揰悢傗夝徚悢摍乯偑偳偆怳傞晳偆偐乮壛朄惈摍乯偲偄偆栤戣丅
5. 戞俆夞丂Lin's nugatory crossing conjecture 寢傃栚K傪岎嵎岎姺偟偰嵞傃K偑摼傜傟偨側傜偽丄偦偺岎嵎偼柍岠側傕偺偵尷傞偲偄偆梊憐丅
6. 戞俇夞丂Cabling conjecture S^3撪偺寢傃栚偵増偭偨僨乕儞庤弍偱丄壜栺側懡條懱偑摼傜傟偨側傜偽丄偦偺寢傃栚偼働乕僽儖寢傃栚偵尷傞偲偄偆梊憐丅
7. 戞俈夞丂Berge conjecture S^3撪偺寢傃栚偵増偭偨僨乕儞庤弍偱丄儗儞僘嬻娫偑摼傜傟偨側傜偽丄偦偺寢傃栚偼僶乕僊寢傃栚偵尷傞偲偄偆梊憐丅
8. 戞俉夞丂Fox's slice-ribbon conjecture 僗儔僀僗寢傃栚偼儕儃儞寢傃栚偱偁傞偲偄偆梊憐丅
9. 戞俋夞丂Kashaev's volume conjecture Kashaev晄曄検乮Colored Jones懡崁幃乯偲寢傃栚曗嬻娫偺憃嬋懱愊偺娫偺娭學幃偵娭偡傞梊憐丅
10. 戞侾侽夞丂Garoufalidis's Jones Slope conjecture 擟堄偺寢傃栚偵娭偟偰丄僕儑乕儞僘僗儘乕僾偺2攞偼忢偵嫬奅僗儘乕僾偱偁傞偲偄偆梊憐丅
11. 戞侾侾夞丂Lopez conjecture 僗儌乕儖側3師尦懡條懱偼僗儌乕儖側寢傃栚傪娷傓偲偄偆梊憐丅
12. 戞侾俀夞丂Neuwirth conjecture 擟堄偺旕帺柧側寢傃栚K偵懳偟偰丄K傪娷傓暵嬋柺F偱丄F伩E(K)偑楢寢偐偮杮幙揑偱偁傞傕偺偑懚嵼偡傞偲偄偆梊憐丅
13. 戞侾俁夞丂Rank versus Genus Conjecture 寢傃栚K偺奜晹E(K)偵偮偄偰丄r(E(K))=g(E(K))偑惉傝棫偮偲偄偆梊憐丅
14. 戞侾係夞丂婜枛僥僗僩 偙傟傑偱妛傫偩偙偲偵偮偄偰僥僗僩偟傑偡丅

嶲峫彂丗

寢傃栚棟榑偺枹夝寛栤戣侾侽

寢傃栚偲嬋柺 Math. Soc. Japan, Sugaku Vol. 67, No. 4 (2015) 403-423