Klaus Jänich

Klaus Werner Jänich (born January 24, 1940 in Dresden ) is a German mathematician .

Klaus Jänich 1976

life and work

Jänich first studied physics and then mathematics in Jena , Tübingen and Bonn and received his doctorate in 1964 from the University of Bonn under Friedrich Hirzebruch with his dissertation vector space bundles and the space of Fredholm operators . In 1965 he worked at Cornell University and 1966/67 at the Institute for Advanced Study in Princeton . Since 1969 he has been a full professor of mathematics at the University of Regensburg .

Jänich has been concerned with algebraic topology and differential topology since the 1960s , where he dealt, among other things, with index theory of differential operators on manifolds , the classification of manifolds (on which differentiable effects exist through transformation groups ) and the theory of singularities of differentiable mappings (" catastrophe theory ") ) employed by René Thom . In 1965 he proved the Atiyah-Jänich theorem assumed by Michael Atiyah . ${\displaystyle G}$ ${\displaystyle G}$

Jänich is known for his pedagogically skilful textbooks, which are limited to the essentials, with many illustrations and detailed explanatory text. His book with Theodor Bröcker on differential topology is a standard textbook that has also been translated into English. In addition, he has always worked with theoretical physicists (in Regensburg and elsewhere) on specific border issues between the disciplines involved.

Fonts

• Function Theory - An Introduction. Springer-Verlag, 6th edition 2004, ISBN 3540203923 .
• Linear Algebra. Springer-Verlag, 10th edition 2007, ISBN 3540402071 .
• Topology. Springer-Verlag, 8th edition 2005, ISBN 978-3-540-21393-2 , doi : 10.1007 / b138142 (General Topology, English translation by Undergraduate Texts in Mathematics, Springer-Verlag, 1984).
• Analysis for physicists and engineers - a textbook for the second year of study - function theory, differential equations, special functions. Springer-Verlag, 4th edition 2001, ISBN 3540419853 .
• Vector analysis. Springer-Verlag, 4th edition 2003, ISBN 3-540-00392-4 , doi : 10.1007 / 978-3-662-10750-8 (explains both the classic terminology and differential forms).
• with Theodor Bröcker: Introduction to the differential topology . Springer-Verlag, Heidelberger Taschenbücher 1973, reprinted 1990, ISBN 3540064613 .
• Mathematics - Written for physicists. 2 volumes, Springer-Verlag, volume 1, 2nd edition 2005, ISBN 3540213929 , volume 2, 2002, ISBN 3540428399 (in volume 2 vector analysis and analysis in several variables).
• Jänich: vector space bundles and the space of the Fredholm operators. (Dissertation), Mathematische Annalen Vol. 161, 1965, pp. 129-142.
• Jänich: Caustics and Catastrophes. Mathematische Annalen Vol. 209, 1974, pp. 161-180.
• Jänich: Symmetry Properties of Singularities of Functions. ${\displaystyle C^{\infty }}$Mathematische Annalen, Volume 238, 1978, pp 147-156.
• Jänich: Characterization of the signature of manifolds by an additivity property. Inventiones Mathematicae Vol. 6, 1968, pp. 35-40.
• Jänich: On the Classification of Manifolds. ${\displaystyle O(n)}$Mathematische Annalen, Vol. 176, 1968, pp. 53-76.

Web links

• Research report of his group in Regensburg
• Klaus Jänich in the Mathematics Genealogy Project (English)