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The Fundamental Group, Covering Spaces and Topology in Biology
Gdansk University of Technology.
Gdansk University of Technology.
2006 (English)In: Conference materials IX International Workshop for Young Mathematicians: Topology, 2006, 19-29 p.Conference paper, Published paper (Other academic)
Abstract [en]

Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber over x, Path lifting Theorem). With the use of the exponential map and the idea of the index of a loop, we show that the fundamental group of the circle S1 is isomorphic to the integers Z with addition. We mention some other interesting fundamental groups (e.g. the fundamental group of a torus or of thefigure eight). We also present some very interesting applications of topological concepts in Molecular Biology.

Place, publisher, year, edition, pages
2006. 19-29 p.
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-241882OAI: oai:DiVA.org:uu-241882DiVA: diva2:781865
Conference
IX International Workshop for Young Mathematicians
Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2015-01-26

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Bartoszek, Krzysztof

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