Algebraic Topology II (ΓΕ6): Διαφορά μεταξύ των αναθεωρήσεων

Αναθεώρηση της 22:00, 10 Νοεμβρίου 2022

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	ΓΕ6
Semester	1
Course Title	Algebraic Topology II
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Special background. Specialized general knowledge. Skills development in connections with topology geometry and algebra.
Prerequisite Courses	ΓΕ5 - Algebraic Topology I
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning outcomes	Algebraic Topology begins its creation by H. Poincare in 1900. In its first thirty years the field seemed limited in application in algebraic geometry, but this changed dramatically in 1930 with the creation of differential topology by G. De Rham and E. Cartan and of homotopy theory by W. Hurewicz and H. Hopf. Its influence began to spread to more and more branches as it gradually took on a central role in mathematics. This course is a continuation of the course Algebraic Topology I and aims in studying and managing advanced skills in order to calculate and solve difficult problems in topology-geometry. The key idea is to attach algebraic structures to topological spaces and their maps in such a away the algebra is both invariant under a variety of deformation of spaces and maps, and computable. Our aim is to transform difficult geometric problems to homotopic ones. We also study and develop homotopical tools. We calculate homological modules as well as cohomological rings for important spaces. Homotopical and cohomological sequences are concerned.
General Competences	Search for analysis and synthesis of data and information related with topological and geometrical problems. Working independently and in a Team work. Working in an interdisciplinary environment aiming at production of new research ideas related to the syllabus of the course.

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+Algebraic Topology begins its creation by H. Poincare in 1900. In its first thirty years the field seemed limited in application in algebraic geometry, but this changed dramatically in 1930 with the creation of differential topology by G. De Rham and E. Cartan and of homotopy theory by W. Hurewicz and H. Hopf. Its influence began to spread to more and more branches as it gradually took on a central role in mathematics. This course is a continuation of the course Algebraic Topology I and aims in studying and managing advanced skills in order to calculate and solve difficult problems in topology-geometry. The key idea is to attach algebraic structures to topological spaces and their maps in such a away the algebra is both invariant under a variety of deformation of spaces and maps, and computable. Our aim is to transform difficult geometric problems to homotopic ones. We also study and develop homotopical tools. We calculate homological modules as well as cohomological rings for important spaces. Homotopical and cohomological sequences are concerned.
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 ! General Competences
 |
-ΧΧΧ
+Search for analysis and synthesis of data and information related with topological and geometrical problems. Working independently and in a Team work. Working in an interdisciplinary environment aiming at production of new research ideas related to the syllabus of the course.
 |}