Krystyna kuperberg biography channel

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The Seifert conjecture

Krystyna’s most fam­ous counter­example is a smooth counter­example to the Seifert con­jec­ture. Au­burn Uni­versity in Alabama offered a solu­tion to their two-body prob­lem; they ar­rived in Au­burn as new fac­ulty mem­bers in 1974. They were both phar­macists and owned a phar­macy in Szczu­cin, a small town near Tarnów.

Zbl:0323.55021.}, ISBN = {9780126634501}, }

Who is Krystyna Kuperberg?

Krystyna M. Kuperberg is a Polish-American mathematician who currentlyworks at Auburn University.

Her parents, Jan W. and Barbara H. Trybulec, were pharmacists and owned a pharmacy in Tarnów.

Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {321}, NUMBER = {1}, YEAR = {1990}, PAGES = {129--143}, DOI = {10.2307/2001594}, NOTE = {MR:989579. Re­lated to this was a draw­ing class in fifth grade, teach­ing per­spect­ive draw­ing.

Krystyna answered a ques­tion of Knas­ter by con­struct­ing a Peano con­tinuum (a com­pact, con­nec­ted, loc­ally con­nec­ted, met­riz­able space) which is to­po­lo­gic­ally ho­mo­gen­eous (the group of homeo­morph­isms is trans­it­ive), but not bi­ho­mo­gen­eous (there are pairs of points that can­not be swapped by a homeo­morph­ism) [7].

krystyna kuperberg biography channel

Am. Math. In 1987 she solved a problem of Knaster concerning bi-homogeneity of continua.

In the 1980s she became interested in fixed points and topological aspects of dynamical systems In 1989 Kuperberg and Coke Reed solved a problem posed by Stan Ulam in the Scottish Book.

The solution to that problem led to her well known 1993 work in which she constructed a smooth counterexample to the Seifert conjecture.

She has since continued to work in dynamical systems Her major lectures include an American Mathematical Society Plenary Lecture in March 1995, an MAA Plenary Lecture in January 1996, and an ICM invited talk in 1998.

Zbl:1158.54014.}, ISSN = {0002-9939}, }

 New York

[15]K. Ku­per­berg: “Two Vi­et­or­is-type iso­morph­ism the­or­ems in Bor­suk’s the­ory of shape, con­cern­ing the Vi­et­or­is–Cech ho­mo­logy and Bor­suk’s fun­da­ment­al groups,” Chapter22, pp.

Seifert him­self es­tab­lished his name­sake con­jec­ture in a neigh­bor­hood of the Hopf flow. If no one solved a prob­lem, then we would go through pa­pers. 604–​610. Krystyna in­stead in­ser­ted a Wilson plug partly in­to it­self so that it breaks its own or­bits.

Am. Math.

The key con­struc­tion be­hind all known counter­examples to any ver­sion of either the Seifert con­jec­ture or Ulam’s prob­lem is a spe­cial flow in a cyl­in­der \( D^2 \times I \) called a plug\( P \). 129–​143. Math.}, FJOURNAL = {Documenta Mathematica}, VOLUME = {Extra Volume}, YEAR = {1998}, PAGES = {831--840}, URL = {https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1998.2/ICM1998.2.ocr.pdf#page=833}, NOTE = {\textit{Proceedings of the {I}nternational {C}ongress of {M}athematicians, volume 2: {I}nvited lectures} (Berlin, 18--27 August 1998).

MR:1670920. No such simple counter­example is evid­ent in the ori­ent­a­tion-re­vers­ing case. Aca­dem­ic Press, New York.