This course is not currently conducted!
Erasmus code: 11.1
ISCED code: 0541
ECTS credits:
unknown
Language:
English
Organized by:
Faculty of Mathematics, Informatics, and Mechanics
Related to study programmes:
Simplicial Homotopy Theory 1000-1M22STH
- Simplicial sets, skeletal filtrations. Limits, colimits and exponential objects of simplicial sets.
- Homotopies, homotopy equivalences, weak homotopy equivalences.
- Kan complexes and Kan fibrations, homotopy limits.
- Cofibrations and homotopy colimits.
- Fibrant replacements and homotopy groups of simplicial sets.
- Simplicial aproximation and equivalence of homotopy theories of simplicial sets and topological spaces.
- Weak factorization systems and model categories. The Kan–Quillen model structure.
Type of course
elective monographs
Requirements
Prerequisites (description)
Familiarity with basics of topology within the scope of the Topology I course. Understanding of the fundamental notions of homotopy theory (homotopy equivalence, fundamental group) as discussed in Topology II. It will be helpful (but not required) to have familiarity with concepts of algebraic topology such as singular homology, CW-complexes and homotopy groups.
Learning outcomes
- Familiarity with basic concepts of homotopy theory in the framework of simplicial sets: homotopies, (weak) homotopy equivalences, fibrations, cofibrations, fibrant replacements.
- Ability to recognize homotopy non-invariant constructions and to approximate them by homotopy invariant ones.
- Understanding of the analogy between the homotopy theories of simplicial sets and topological spaces.
Assessment criteria
Participation in classes, written homework assignments and oral exam.
Bibliography
- Paul Goerss, John F. Jardine Simplicial homotopy theory 1999
- André Joyal, Myles Tierney An Introduction to Simplicial Homotopy Theory
- André Joyal, Myles Tierney Notes on simplicial homotopy theory
- Peter May Simplicial objects in algebraic topology 1967
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: