SF2721, Topologi, vt 2009 Kursansvarig: Björn Gustafsson, 08-790 7418, gbjorn@math.kth.se Start: Tuesday, January 27, 13.15-15.00, seminar room 3733.

This side will be regularly updated.

New information:

• Examination and registration of grades is now finished for those students (21) who have handed in both sets of homework problems.
  It is still possible to complete the course by handing in homework, but the registering of results will then be in the fall.
  Have a nice summer! /Björn

• The list of homework problems has been slightly revised: problem 8 (on the 14 different sets) in the previous list has been removed (because it was not really interesting), so the numbering is now a little different.

• The lecturing part of the course as finished now, but there still remains some examination.
  Last Tuesday (April 28) we discussed solutions of homework problems 1-15, and next Tuesday (May 5),
  if there is any interest, we may discuss homework problems 16-26.
  At least one student, who has been notified, will present some solutions.

• If you find the home work problems too hard (some of them are indeed difficult) you may replace part or all of them by problems from some textbook.
  For example, the following problems from Armstrong (1983) might be suitable.
  
  • First set (hand-in date March 17): Ch.2: 2, 3, 14, 17, 20, 31, 32. Ch.3: 1, 2, 9, 23, 28, 32, 38. Ch.4: 2, 5, 26, 28.
  • Second set (hand-in date April 21): Ch.5: 1, 5, 11, 15, 21, 25, 37. Ch.6: 1, 13. Ch.7: 2, 3, 27, 33. Ch.8: 7, 12, 14.

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  General information:

  • Credit: 7.5 points (ECTS) in the engineering programme or in the doctoral programme.
  • Language: English or Swedish, depending on audience.

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  Teacher and examinator:

  Björn Gustafsson (gbjorn@kth.se), phone 08-7907418, room 3638.
  
  

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  Literature:

  Basic text:

  M.A. Armstrong: Basic Topology, Undergraduate Texts in Mathematics, Springer Verlag, 1983.

  Side texts:

  C.Adams, R. Franzosa: Introduction to Topology, Pure and Applied, Pearson, Prentice Hall, 2008.
  This is a new and relatively elementary textbook, with a lot of pictures, examples, exercises and applications (even to subjects such as economics and chemistry).

  A. Hatcher: Algebraic Topology, Cambridge University Press, 2002. (Available on the web, 544 pages.)
  This seems to be a very readable text on algebraic topology, however going far beyond the present course.

  O.Ya. Viro, O.A. Ivanov, N.Yu. Netsvetaev, V.M. Kharlamov: Elementary Topology Problem Textbook. (Available on the web, 400 pages.)
  This text on "elementary" topology is based on examples and exercises, hence offers an alternative way of learning the subject .

  Some older books:

  S. Willard: General Topology, Addison-Wesley, 1970.
  A good textbook on pointset topology.

  J. Hocking, G. Young: Topology, Addison-Wesley, 1961.
  A good treatment of both algebraic and pointset topology.

  J.L. Kelley: General Topology, Van Nostrand, 1955.
  A classical text on pointset topology.

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  Description of the course:

  In general, see studiehandboken.

  This is a first course in topology, covering basic pointset topology and some parts of algebraic topology.

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  Examination:

  Essentially by handing in homework problems. The present version is here: homework 2009. (It essentially agrees with an old list, homework 1998.)
  One of the homework problems involves the notion of a filter. See Kelley: General Topology, p. 83 for the definition.

  To pass the course you should hand in correct and well-written solutions of approximately half of the problems. For higher grades more will be needed.
  Oral examination may also be used in some cases.

  Suggested hand-in dates:

  For problems 1-14: March 15.

  For problems 15-25: April 21.

   

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  Preliminary schedule  
   

  Lecture no.	Time and place	Topic	Remarks
  F1	Tuesday, January 27, 13-15, room 3733	Introduction (Ch. 1 in Armstrong)
  F2	Tuesday, February 3, 13-15, room 3733	Basic notions in topology (Ch. 2)
  F3	Tuesday, February 10, 13-15, room 3733	Compactness and product spaces (Ch. 3)
  F4	Tuesday, February 17, 13-15, room 3733	Continuation of previous lecture (Ch. 3)
  F5	Tuesday, February 24, 13-15, room 3733	Connectedness (Ch. 3)
  F6	Tuesday, March 3, 13-15, room 3733	Identification topologies (Ch. 4)
  F7	Tuesday, March 10, 13-15, room 3733	Continuation of previous lectures
  F8	Tuesday, March 17, 13-15, room 3733	The fundamental group (Ch. 5)	First set of home work problems to be handed in
  F9	Tuesday, March 24, 13-15, room 3733	Covering spaces (Ch 5)
  F10	Tuesday, March 31, 13-15, room 3733	Covering transformations. Fixed point theorems.
  F11	Tuesday, April 14, 13-15, room 3733	Triangulation, simplicial approximation (Ch. 6)
  F12	Tuesday, April 21, 13-15, room 3733	The edge group. Classification of surfaces (Ch. 7)	Second set of home work problems to be handed in
  F13	Tuesday, April 28, 13-15, room 3733	Discussion of homework problems 1-15.	Partly presentations by students.
  F14	Tuesday, May 5, 13-15, room 3733	Discussion of homework problems 16-26.	Partly presentations by students.