V. M. Buchstaber, “The Chern–Dold character in cobordisms. I”, Math. USSR-Sb., 12:4 (1970), 573

Mathematics of the USSR-Sbornik

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Sb.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Mathematics of the USSR-Sbornik, 1970, Volume 12, Issue 4, Pages 573–594
DOI: https://doi.org/10.1070/SM1970v012n04ABEH000939 (Mi sm3530)

This article is cited in 43 scientific papers (total in 46 papers)

The Chern–Dold character in cobordisms. I

V. M. Buchstaber

English version PDF (1172 kB) Citations (46) Russian version article

References:

PDF

HTML

DOI: https://doi.org/10.1070/SM1970v012n04ABEH000939

Abstract: The fundamental results of the paper are
a) derivation of formulas for the Chern–Dold character

{c h}^{U}

$\mathrm{ch}^U$ and

{c h}_{U}

$\mathrm{ch}_U$ in the theory of universal bordisms

U_{*}

$U_*$ and cobordisms

U^{*}

$U^*$ , respectively;
b) derivation of the formula of a series over the ring

Ω_{u}^{*}

$\Omega^*_u$ which gives addition in the formal group of “geometric” cobordisms, and derivation of the formula for the series

k Ψ_{U}^{k} (u)

$k\Psi^k_U(u)$ , where

u \in U^{2} (C P_{k}^{\infty})

$u\in U^2(CP^\infty_k)$ and the

Ψ_{U}^{k}

$\Psi^k_U$ are Adams operators in

U^{*}

$U^*$ -theory.
Bibliography: 12 titles.

Received: 07.04.1970

Bibliographic databases:

Document Type: Article

UDC: 513.836

MSC: 57R77, 55N22, 19L41, 57R20

Language: English

Original paper language: Russian

Citation: V. M. Buchstaber, “The Chern–Dold character in cobordisms. I”, Math. USSR-Sb., 12:4 (1970), 573–594

Citation in format AMSBIB

\Bibitem{Buc70}

\by V.~M.~Buchstaber

\paper The Chern--Dold character in cobordisms.~I

\jour Math. USSR-Sb.

\yr 1970

\vol 12

\issue 4

\pages 573--594

\mathnet{http://mi.mathnet.ru/eng/sm3530}

\crossref{https://doi.org/10.1070/SM1970v012n04ABEH000939}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=273630}

\zmath{https://zbmath.org/?q=an:0204.23503|0219.57027}

Linking options:

https://www.mathnet.ru/eng/sm3530

https://doi.org/10.1070/SM1970v012n04ABEH000939

https://www.mathnet.ru/eng/sm/v125/i4/p575

This publication is cited in the following 46 articles:

V. M. Buchstaber, F. Yu. Popelenskii, “Cohomology of Hopf algebras and Massey products”, Russian Math. Surveys, 79:4 (2024), 567–648
V. M. Buchstaber, F. Yu. Popelensky, “Cohomology of the Heisenberg Manifold Sequence”, J Math Sci, 284:1 (2024), 17
V. M. Buchstaber, A. P. Veselov, “Todd Polynomials and Hirzebruch Numbers”, Proc. Steklov Inst. Math., 325 (2024), 74–85
Domenico Fiorenza, Hisham Sati, Urs Schreiber, “Twistorial cohomotopy implies Green–Schwarz anomaly cancellation”, Rev. Math. Phys., 34:05 (2022)
V. M. Buchstaber, “Partially framed manifolds and loop spaces on the group $\operatorname{SU}(2)$”, Russian Math. Surveys, 75:4 (2020), 782–784
T. Ayano, V. M. Buchstaber, “Analytical and number-theoretical properties of the two-dimensional sigma function”, Chebyshevskii sb., 21:1 (2020), 9–50
John Lind, Hisham Sati, Craig Westerland, “Twisted iterated algebraic K-theory and topological T-duality for sphere bundles”, Ann. K-Th., 5:1 (2020), 1
V. M. Buchstaber, I. Yu. Limonchenko, “Massey products, toric topology and combinatorics of polytopes”, Izv. Math., 83:6 (2019), 1081–1136
Malkhaz Bakuradze, Vladimir V. Vershinin, “On Addition Theorems Related to Elliptic Integrals”, Proc. Steklov Inst. Math., 305 (2019), 22–32
A. A. Gaifullin, “Small covers of graph-associahedra and realization of cycles”, Sb. Math., 207:11 (2016), 1537–1561
A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590
V. M. Buchstaber, “Complex cobordism and formal groups”, Russian Math. Surveys, 67:5 (2012), 891–950
V. M. Buchstaber, E. Yu. Bun'kova, “Krichever Formal Groups”, Funct. Anal. Appl., 45:2 (2011), 99–116
V. M. Buchstaber, “The general Krichever genus”, Russian Math. Surveys, 65:5 (2010), 979–981
Buchstaber V., Panov T., Ray N., “Toric Genera”, International Mathematics Research Notices, 2010, no. 16, 3207–3262
D. V. Millionshchikov, “Algebra of Formal Vector Fields on the Line and Buchstaber's Conjecture”, Funct. Anal. Appl., 43:4 (2009), 264–278
A. A. Kustarev, “Singularity cycles and characteristic classes in cobordism”, Russian Math. Surveys, 62:5 (2007), 999–1001
G. A. Merzon, “Realization of formal groups by cohomology theories, and the Adams–Novikov operations”, Russian Math. Surveys, 62:4 (2007), 813–815
I. Panin, A. Smirnov, Axiomatic, Enriched and Motivic Homotopy Theory, 2004, 261
A. A. Bolibrukh, A. P. Veselov, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, S. P. Novikov, T. E. Panov, Yu. M. Smirnov, “Viktor Matveevich Buchstaber (on his 60th birthday)”, Russian Math. Surveys, 58:3 (2003), 627–635

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

Математический сборник (новая серия) - 1964–1988

Statistics & downloads:
Abstract page:	1032
Russian version PDF:	385
English version PDF:	74
References:	91
First page:	4

Registration to the website

Logotypes