R. Chatterjee
Wintersemester 2022/23
Dienstag 14-15:30, Seminarraum 3
Wie halte ich einen guten Seminarvortrag?
(von Prof. Manfred Lehn)
Knot theory has transformed over the years from a specialised branch of
topology to a very popular area of study in mathematics.
In the early 20th century, topologists studied knots from the point of view
of knot groups and invariants from homology. More recently, many breakthrough
results about knot theory established its connection with physics, algebraic
geometry, quantum theory etc.
The goal of this seminar is to have a basic understanding of knot theory, and then to study the special knots in contact manifolds called Legendrian and transverse, respectively. No prior knowledge of contact geometry will be assumed.
Vorträge (Talks will be in English):
11.10.22 | Introduction to smooth knot theory I [R 1, 3C], [A 3] (definition, knot equivalence, isotopy, knot diagrams, mirrors, knot invariants, the unknot and torus knots) Rima Chatterjee |
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18.10.22 | Introduction to smooth knot theory II [R 5 A, D],
[A 1.2, 1.3, 4] (genus, Seifert's algorithm, connected sum, prime vs non-prime knots, linking number, Reidemeister moves) Rima Chatterjee |
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25.10.22 | Introduction to smooth knot theory III [R 3 A, B, D],
[A 9] (the knot group, knot complement and homology, Wirtinger presentation trefoil is not the unknot) Humay Khalilova |
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1.11.22 | no seminar | ||||||
8.11.22 | Introduction to contact topology and Legendrian
and transverse knots [G 2.1, 3.1, 3.2], [E 2.1 - 2.4] Ilona Schlömer |
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15.11.22 | Classical invariants of Legendrian and transverse knots
[G 3.5], [E 2.5 - 2.7] Fabian Bühner |
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22.11.22 | Introduction to convex surfaces [G 4.8], [E 2.8] Norman Thies |
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29.11.22 | Tight vs overtwisted, and Bennnequin inequality [E 2.9, 3],
[G 4.5, 4.6.5] Tilman Becker |
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6.12.22 | Classification of Legendrian and transverse knots [EH] Rima Chatterjee |
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There is the option for three more talks in January |
Literatur:
[A] | C. Adams: Freeman, 1994. |
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[E] | J. B. Etnyre: Legendrian and transversal knots,
Elsevier, 2005. |
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[EH] | J. B. Etnyre, K. Honda: Knots and contact geometry I -
Torus knots and the figure eight knot, |
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[G] | H. Geiges: Cambridge University Press, 2008. |
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[PS] | V. V. Prasolov, A. B. Sossinsky: American Mathematical Society, 1997. |
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[R] | D. Rolfsen: Publish or Perish, 1990. |