19223811 Seminar

SoSe 19: Research Module: Topology

Holger Reich

Additional information / Pre-requisites

Prerequisites: Familiarity with basic concepts of Algebraic Topology

Comments

Cobordismtheory

An element in the $n$th cobordism group $Nn(X)$ is represented by a map from an $n$-dimensional compact manifold without boundary into $X$. Two such maps are called bordant and represent the same element, if the two maps can be extended to a map on an $n+1$-dimensional manifold, whose boundary is the disjoint sum of the two $n$-dimensional manifolds. The funtor $N ( - )$ that arises in this simple geometric fashion is a generalized homology theory. Already when $X$ is a point the group $N( pt)$ is interesting.

The aim of the seminar is to compute the bordism ring $N ( pt )$. Along the way we will define many mathematical objects and learn to work with them: basic concepts from differential topology, the Pontrjagin-Thom construction, spectra, characteristic classes, formal groups, ...

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Suggested reading

Literature:
Thedor Bröcker, Tammo tom Dieck: Kobordismentheorie, Lecture Notes in Mathematics 178, Springer-Verlag

14 Class schedule

Regular appointments

Tue, 2019-04-09 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-04-16 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-04-23 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-04-30 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-05-07 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-05-14 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-05-21 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-05-28 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-06-04 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-06-11 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-06-18 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-06-25 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-07-02 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

Tue, 2019-07-09 14:00 - 16:00

Lecturers:
Univ.-Prof. Dr. Holger Reich
Univ.-Prof. Dr. Elmar Vogt

Location:
A3/SR 210 Seminarraum (Arnimallee 3-5)

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