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2010年度後期「MMA数学特論II」
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担当教員： Craig Pastro 教員
開講時限： 木曜2限（10:30～12:00）
対象学年： MMA修士およびその他の数理学修士
特記事項： 講義やその他の伝達はすべて英語で行われます。
テキスト（参照用）
Christian Kassel and Vladimir Turaev "Braid Groups" (Springer GTM)
授業ログ
Oct. 7, 2010 / #1 Some Basic Algebra I
- Monoids, Groups, and Def. of Braid Groups
Oct. 14, 2010 / #2 Some Basic Algebra II
- Symmetric Groups, Rings, Algebras and Modules
- Next class will be held on Nov. 4th.
Oct. 21st and 28th are CANCELLED.
Nov. 4, 2010 / #3 Introduction to Braid Groups I
- Definition of Braid Groups from Symmetric Groups (dropped one of properties -> non-abelian)
- (Special) Pure Braid Groups
- PBGs generate BGs
Nov. 11, 2010 / #4 Introduction to Braid Groups II
- Section and Retraction
- Combed Form
- Theorem: Z(Bn)=Z(Pn) is an infinite cyclic gp (\theta generator).
Nov. 18, 2010 / #5 Knots and Links
- Mapping Class Group: Isotopic, Homeomorphic
- Knots and Links
- Alexander's Theorem: Any oriented link in R^3 is isotopic to a closed braid.
Dec. 2, 2010 / #6 Alexander's Theorem and Markov's theorem
- Proof of Alexander's Theorem
- Markov's theorem
- Markov Functions
Dec. 9, 2010 / #7 Yang-Baxter equation
- Yang-Baxter equation
- Monoids and groups of fractions
Dec. 16, 2010 / #8 Monoids
- Divisibility in monoids, Monoid presentations
- Word problem and divisibility problem for monoid presentations
- Solution to the word and divisibility problem for finite weighted monoids
Jan. 6, 2011 / #9 TQFT I
- Introduction to TQFT
- Manifolds, Cobordisms
Jan. 13, 2011 / #10 TQFT II
- Cobordisms (conti.)
- Frobenius Algebra
- Final Remarks
