MU04062 Algebraic and Differential Topology I

Mathematical Institute in Opava
Winter 2012
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Marvan, CSc. (lecturer)
doc. RNDr. Michal Marvan, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Prerequisites
Tady jsou uvedené předpoklady ENG
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Algebraic topology studies topological spaces by algebraic means. Among its typical problems is the issue of finding out whether on topological space can be continuously mapped onto another. A positive answer may be obtained by constructing such a map but a negative answer may be more difficult to get. In this four-term course on algebraic topology, algebraic methods to solve such problems will be consecutively acquired. This first term, the foundations of homotopy are taught. Homotopies will be met during all four terms of the course. Minimal preliminary knowledge on topology and algebraic structures will be sufficient.
Syllabus
  • Categories, functors, category Top, Gr a Ab; products and sums, pull-back and push-out.
    Homotopy of continuous mappings, relative homotopy; homotopical equivalence of topological spaces, contractibility.
    Category Top_h, functors in algebraic topology, elementary problems of algebraic topology, homotopy extension property, Borsuk pairs.
    Paths and loops, fundamental group, simply-connected spaces.
    Covering spaces, covering path theorem, covering homotopy theorem, fundamental group, covering mapping theorem
    Methods of calculation of homotopy groups, G-spaces, fundamental group of the orbit space; Seifert-Van Kampen theorem.
    Superior homotopic groups, exact sequence of the homotopic groups.
Literature
    recommended literature
  • Häberle, G.:. Technika životního prostředí pro školu i praxi. Praha, 2003. info
  • C. Kosniowski. A First Course in Algebraic Topology. 1980. ISBN 0521298644. info
  • S. Mac Lane. Categories for the Working Mathematician. New York, 1971. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Tady jsou uvedeny požadavky na studenta ENG.
The course is also listed under the following terms Winter 1997, Summer 1998, Winter 1998, Summer 1999, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2012, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2012/MU04062