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Kavli IPMU Komaba Seminar
Seminar information archive ～04/22｜Next seminar｜Future seminars 04/23～
| Date, time & place | Monday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|
2008/04/08
10:30-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Akihiro Tsuchiya (IPMU, The University of Tokyo)
IPMU Komaba Lectures,Homotopy Theory (before 1970)
Akihiro Tsuchiya (IPMU, The University of Tokyo)
IPMU Komaba Lectures,Homotopy Theory (before 1970)
[ Abstract ]
Tuesday, April -- July, 2008
First Lecture Aprl 8
Recently the notion of homotopy theory has been widely used in many areas of
contemporary mathematics including mathematical physics.
The purpose of the lectures is to present an overview of the developments
of homotopy theory mainly from 1940's through 1960's, partly in view of
more recent progress in other areas.
(1) Prehistory of homotopy theory
-- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem
(2) Eilenberg-MacLane space and Postnikov system
(3) Steenrod algebras
(4) Serre's theorem on the homotopy groups of spheres
(5) Rational homotopy theory
(6) Stable homotopy category and Adams spectral sequence
(7) Vector bundles and characteristic classes
(8) Complex cobordism and Quillen's theorem
(9) Miscellaneous topics
Rereferences :
(1) J.P.May, A Concise Course in Algebraic Topology,
The University of Chicago Press
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres
The second edition, AMS Chelsea Series
http://www.math.rochester.edu/u/faculty/doug/mu.html
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra
Tuesday, April -- July, 2008
First Lecture Aprl 8
Recently the notion of homotopy theory has been widely used in many areas of
contemporary mathematics including mathematical physics.
The purpose of the lectures is to present an overview of the developments
of homotopy theory mainly from 1940's through 1960's, partly in view of
more recent progress in other areas.
(1) Prehistory of homotopy theory
-- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem
(2) Eilenberg-MacLane space and Postnikov system
(3) Steenrod algebras
(4) Serre's theorem on the homotopy groups of spheres
(5) Rational homotopy theory
(6) Stable homotopy category and Adams spectral sequence
(7) Vector bundles and characteristic classes
(8) Complex cobordism and Quillen's theorem
(9) Miscellaneous topics
Rereferences :
(1) J.P.May, A Concise Course in Algebraic Topology,
The University of Chicago Press
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres
The second edition, AMS Chelsea Series
http://www.math.rochester.edu/u/faculty/doug/mu.html
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra
