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 Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 3, Pages 667–681 (Mi izv2031)

Bott periodicity from the point of view of an $n$-dimensional Dirichlet functional

A. T. Fomenko

Abstract: The paper investigates topological effects associated with an $n$-dimensional Dirichlet functional on spaces of representations of disks with fixed boundaries in compact Lie groups $U(n)$, $O(n)$ or $S_p(n)$. It turns out that the classical Bott periodicity arises naturally when one considers the set of points at which the Dirichlet functional attains an absolute minimum, and the periodicity isomorphism is obtained using this approach “in one step” and not in several steps as it was the case when the one-dimensional action functional on the space of loops was used.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:3, 681–695

Bibliographic databases:

UDC: 513.83
MSC: Primary 49F15; Secondary 58E05

Citation: A. T. Fomenko, “Bott periodicity from the point of view of an $n$-dimensional Dirichlet functional”, Izv. Akad. Nauk SSSR Ser. Mat., 35:3 (1971), 667–681; Math. USSR-Izv., 5:3 (1971), 681–695

Citation in format AMSBIB
\Bibitem{Fom71} \by A.~T.~Fomenko \paper Bott periodicity from the point of view of an $n$-dimensional Dirichlet functional \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1971 \vol 35 \issue 3 \pages 667--681 \mathnet{http://mi.mathnet.ru/izv2031} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=293673} \zmath{https://zbmath.org/?q=an:0223.58007} \transl \jour Math. USSR-Izv. \yr 1971 \vol 5 \issue 3 \pages 681--695 \crossref{https://doi.org/10.1070/IM1971v005n03ABEH001101} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. A. Aminov, “On the instability of a minimal surface in an $n$-dimensional Riemannian space of positive curvature”, Math. USSR-Sb., 29:3 (1976), 359–375
2. A. T. Fomenko, “Multi-dimensional variational methods in the topology of extremals”, Russian Math. Surveys, 36:6 (1981), 127–165
3. A. V. Tyrin, “On the absence of local minima in the multi-dimensional Dirichlet functional”, Russian Math. Surveys, 39:2 (1984), 207–208
4. A. V. Tyrin, “Critical points of the multidimensional Dirichlet functional”, Math. USSR-Sb., 52:1 (1985), 141–153
5. A. A. Tuzhilin, “Morse-type indices of of two-dimensional minimal surfaces in $\mathbf R^3$ and $\mathbf H^3$”, Math. USSR-Izv., 38:3 (1992), 575–598
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