The Fundamental Group, Covering Spaces and Topology in Biology
2006 (English)In: Conference materials IX International Workshop for Young Mathematicians: Topology, 2006, 19-29 p.Conference paper (Other academic)
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.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-241882OAI: oai:DiVA.org:uu-241882DiVA: diva2:781865
IX International Workshop for Young Mathematicians