Guido Mislin

Mislin completed his undergraduate studies and diploma in Mathematics in 1964 and received his Ph.D. in 1967 from ETH Zūrich. He then moved to U.S. and completed his post-doctoral studies from Cornell University and University of California, Berkeley.{{cn|date=January 2021}}

Following his post-doctoral studies, Mislin was appointed as an assistant professor at the Ohio State University. In 1972, he moved back to Switzerland and joined ETH Zurich as an Associate Professor of Mathematics. He was promoted to Professor of Mathematics in 1979. Mislin headed the Department of Mathematics from 1998 till 2002. He retired in 2006 and was gifted with Guido's Book of Conjectures, which is a collection of short notes written by 91 different authors.{{Cite web|url=http://www.unige.ch/math/EnsMath/EM_MONO/m40.html|title=Monograph 36|website=www.unige.ch}} Mislin is associated with ETH Zurich as a Professor Emeritus of Mathematics.

Mislin specializes in algebraic topology, and has conducted research focusing especially on questions regarding general localization theory. He has also worked on cohomology of groups and algebraic K-Theory of group rings.

Mislin studied the cohomology of classifying spaces of complex Lie groups and related discrete groups. His work proved that the Generalized Isomorphism Conjecture is equivalent to a Finite Subgroup Conjecture, generalizing earlier results due to Mark Feshbach and John Milnor, without using Becker-Gottlieb transfer.{{Cite journal|url=https://doi.org/10.1007/BF02566356|title=Cohomology of classifying spaces of complex Lie groups and related discrete groups|first1=Eric M.|last1=Friedlander|first2=Guido|last2=Mislin|date=December 1, 1984|journal=Commentarii Mathematici Helvetici|volume=59|issue=1|pages=347–361|via=Springer Link|doi=10.1007/BF02566356|s2cid=121400667|url-access=subscription}} He presented a theorem regarding constructing torsion classes in systemic manner, by using Chern classes of canonical representation. He discussed the results and also proved certain properties regarding the Chern classes of representations of cyclic groups.{{cite journal

| last1 = Glover | first1 = H.

| last2 = Mislin | first2 = G.

| department = Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985)

| doi = 10.1016/0022-4049(87)90023-5

| issue = 1-3

| journal = Journal of Pure and Applied Algebra

| mr = 885103

| pages = 177–189

| title = Torsion in the mapping class group and its cohomology

| url = https://core.ac.uk/reader/82337950

| volume = 44

| year = 1987}}

Mislin authored a paper in 1990s regarding group homomorphisms inducing mod-p cohomology isomorphisms and highlighted the conditions on p in group theoretic terms for p to induce an H'Z/p-isomorphism.{{Cite journal|url=https://doi.org/10.1007/BF02566619|title=On group homomorphisms inducing mod-p cohomology isomorphisms|first=Guido|last=Mislin|date=December 1, 1990|journal=Commentarii Mathematici Helvetici|volume=65|issue=1|pages=454–461|via=Springer Link|doi=10.1007/BF02566619|s2cid=121317779|url-access=subscription}} He applied the concept of satellites in order to define Tate cohomology groups for an arbitrary group G and G-module M.{{Cite journal|title=Tate cohomology for arbitrary groups via satellites|first=Guido|last=Mislin|date=April 5, 1994|journal=Topology and Its Applications|volume=56|issue=3|pages=293–300|doi=10.1016/0166-8641(94)90081-7|doi-access=free}}

Mislin focused on Bass conjecture and conducted a study to prove that the Bost Conjecture on the L1-assembly map for discrete groups implies the Bass Conjecture.{{Cite journal|url=https://doi.org/10.1007/s00208-004-0521-6|title=From acyclic groups to the Bass conjecture for amenable groups|first1=A. J.|last1=Berrick|first2=I.|last2=Chatterji|first3=G.|last3=Mislin|date=August 1, 2004|journal=Mathematische Annalen|volume=329|issue=4|pages=597–621|via=Springer Link|doi=10.1007/s00208-004-0521-6|arxiv=1004.1941|s2cid=11054222}} He reformulated the weak Bass Conjecture as a comparison of ordinary and L2-Lefschetz numbers.{{Cite web|url=https://msp.org/gtm/2007/10/gtm-2007-10-002p.pdf|title=Homotopy idempotents on manifolds and Bass' conjectures}}

Mislin studied and extended the work conducted by several authors on theory of topological localization.{{Cite journal|url=https://academic.oup.com/plms/article/s3-26/4/693/1504965|title=Homotopical Localization|first1=Peter|last1=Hilton|first2=Guido|last2=Mislin|first3=Joseph|last3=Roitberg|date=June 1, 1973|journal=Proceedings of the London Mathematical Society|volume=s3-26|issue=4|pages=693–706|via=academic.oup.com|doi=10.1112/plms/s3-26.4.693|url-access=subscription}} He presented new results to the theory which were then applied to other studies.{{Cite journal|doi=10.1090/S0002-9904-1972-13110-0|s2cid=51796120|title=Topological localization and nilpotent groups|year=1972|last1=Hilton|first1=Peter|last2=Mislin|first2=Guido|last3=Roitberg|first3=Joseph|journal=Bulletin of the American Mathematical Society|volume=78|issue=6|pages=1060–1064|doi-access=free}} Mislin also presented a periodicity theorem and proved the various properties of homotopy groups of K-theory localization.{{Cite journal|title=Localization with respect to K-theory|first=G.|last=Mislin|date=November 1, 1977|journal=Journal of Pure and Applied Algebra|volume=10|issue=2|pages=201–213|doi=10.1016/0022-4049(77)90023-8|doi-access=free}}

• 1968 - Silver Medal, ETH Zurich{{cn|date=December 2020}}

• Localization of Nilpotent Groups and Spaces (1975) {{ISBN|978-1483258744}}
• Proper Group Actions and the Baum-Connes Conjecture (Advanced Courses in Mathematics - CRM Barcelona) (2003) {{ISBN|978-3764304089}}

• Mislin, G. (1994). Tate cohomology for arbitrary groups via satellites. Topology and its Applications, 56(3), 293–300.
• Kropholler, P. H., & Mislin, G. (1998). Groups acting on finite dimensional spaces with finite stabilizers. Commentarii Mathematici Helvetici, 73(1), 122–136.
• Friedlander, E. M., & Mislin, G. (1984). Cohomology of classifying spaces of complex Lie groups and related discrete groups. Commentarii Mathematici Helvetici, 59(1), 347–361.
• Mislin, G. (1990). On group homomorphisms inducing mod-p cohomology isomorphisms. Commentarii Mathematici Helvetici, 65(1), 454–461.
• Mislin, G. (1974). Nilpotent groups with finite commutator subgroups. In Localization in Group Theory and Homotopy Theory (pp. 103–120). Springer, Berlin, Heidelberg.

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Category:Living people

Category:1941 births

Category:ETH Zurich alumni

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Category:Swiss mathematicians