Bulletin of the American Mathematical Society
- Bull. Amer. Math. Soc.
- Volume 72, Number 3 (1966), 358-426.
Whitehead torsion
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Source
Bull. Amer. Math. Soc., Volume 72, Number 3 (1966), 358-426.
Dates
First available in Project Euclid: 4 July 2007
Permanent link to this document
https://projecteuclid.org/euclid.bams/1183527946
Mathematical Reviews number (MathSciNet)
MR0196736
Zentralblatt MATH identifier
0147.23104
Citation
Milnor, J. Whitehead torsion. Bull. Amer. Math. Soc. 72 (1966), no. 3, 358--426. https://projecteuclid.org/euclid.bams/1183527946
References
- E. E. Kummer, 1851 Sur la théorie des nombres complexes composés de racines de l'unitê et de nombres entiers, J. Math. (Liouville) 16, 377-498.
- E. E. Kummer, 1860 Bemerkungen zu den aus 29ten Einheitswurzeln gebildeten Zahlen, Monatsber. K. Akad. Wiss. Berlin, 734-735.
- E. E. Kummer, 1870 Über eine Eigenschaft der Einheiten der aus den Wurzeln der Gleichung αλ = 1 gebildeten complexen Zahlen und über den zweiten Faktor der Klassenzahl, Monatsber. K. Akad. Wiss. Berlin, 855-880.
- E. E. Kummer, 1874 Über diejenigen Primzahlen λ, filr welche die Klassenzahl der aud λ-ten Einheitswurzeln gebildeten complexen Zahlen durch λ theilbar ist, Monatsber. K. Akad. Wiss. Berlin, 239-248.
- G. G. Reuschle, 1875 Tafeln complexer Primzahlen welche aus Wurseln der Einheit gebildet sind, Berlin K. Akad. Wiss.
- P. Wolfskehl, 1886 Beweis dass der zweite Faktor der Klassenanzahl für die aus den elften und dreizehnten Einheitswurzeln gebildeten Zahlen gleich Eins ist, J. Riene Angew. Math. 99, 173-178.
- H. Minkowski, 1891 Ueber die positiven quadratischen Formen und über kettenbruchähnliche Algorithmen, J. Reine Angew. Math. 107, 278-297.
- A. Hurwitz, 1895 Die unimodularen Substitutionen in einem algebraischen Zahlenkörper, Mathematische Werke 2, 244-268.
- H. S. Vandiver and G. E. Wahlin, 1928 Algebraic numbers. II, Bull. Nat. Res. Council, 62.
- W. Franz, 1935 Über die Torsion einer Überdeckung, J. Reine Angew. Math. 173, 245-254.Zentralblatt MATH: 0012.12702
- K. Reidemeister, 1935 Homotopieringe und Linsenräume, Hamburger Abhandl. 11, 102-109.
- M. Rueff, 1938 Beiträge sur Untersuchung der Abbildungen von Mannigfaltigkeiten, Compositio Math. 6, 161-202.
- G. de Rham, 1939 Sur les complexes avec automorphismes, Comment. Math. Helv. 12, 191-211.
- J. H. C. Whitehead, 1939 Simplicial spaces, nuclei and m-groups, Proc. London Math. Soc. 45, 243-327.
- G. Higman, 1940 The units of group rings, Proc. London Math. Soc. 46, 231-248.
- J. H. C. Whitehead, 1940 On C1- complexes, Ann. of Math. 41, 809-824.Zentralblatt MATH: 0025.09203
Mathematical Reviews (MathSciNet): MR2545
Digital Object Identifier: doi:10.2307/1968861 - J. H. C. Whitehead, 1941 On incidence matrices, nuclei and homotopy types, Ann. of Math. 42, 1197-1239.Zentralblatt MATH: 0063.08227
Mathematical Reviews (MathSciNet): MR5352
Digital Object Identifier: doi:10.2307/1970465 - J. Dieudonné, 1943 Les determinants sur un corps non commutatif, Bull. Soc. Math. France 71, 27-45.
- C. L. Siegel, 1943 Discontinuous groups, Ann. of Math. 44, 674-689.Zentralblatt MATH: 0061.04504
Mathematical Reviews (MathSciNet): MR9959
Digital Object Identifier: doi:10.2307/1969104 - J. H. C. Whitehead, 1949 Combinatorial homotopy. I, Bull. Amer. Math. Soc. 55, 213-245.Zentralblatt MATH: 0040.38704
Mathematical Reviews (MathSciNet): MR30759
Digital Object Identifier: doi:10.1090/S0002-9904-1949-09175-9
Project Euclid: euclid.bams/1183513543 - K. Reidemeister, 1950 Complexes and homotopy chains, Bull. Amer. Math. Soc. 56, 297-307.Zentralblatt MATH: 0037.39602
Mathematical Reviews (MathSciNet): MR36506
Digital Object Identifier: doi:10.1090/S0002-9904-1950-09404-X
Project Euclid: euclid.bams/1183514830 - G. de Rham, 1950 Complexes à automorphismes et homéomorphie différentiables, Ann. Inst. Fourier, Grenoble 2, 51-67.Zentralblatt MATH: 0043.17601
Mathematical Reviews (MathSciNet): MR43468
Digital Object Identifier: doi:10.5802/aif.19 - J. H. C. Whitehead, 1950 Simple homotopy types, Amer. J, Math. 72, 1-57.Zentralblatt MATH: 0040.38901
Mathematical Reviews (MathSciNet): MR35437
Digital Object Identifier: doi:10.2307/2372133 - H. Hasse, 1952 Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin.
- I. Kaplansky, 1952 Modules over Bedekind rings and valuation rings, Trans. Amer. Math. Soc. 72, 327-340.Zentralblatt MATH: 0046.25701
Mathematical Reviews (MathSciNet): MR46349
Digital Object Identifier: doi:10.1090/S0002-9947-1952-0046349-0 - P. Olum, 1953 Mappings of manifolds and the notion of degree, Ann. of Math. 58, 458-480.Zentralblatt MATH: 0052.19901
Mathematical Reviews (MathSciNet): MR58212
Digital Object Identifier: doi:10.2307/1969748 - E. Artin, 1957 Geometric algebra, Interscience, New York.
- I. Reiner, 1958 Normal subgroups of the unimodular group, Illinois J. Math. 2, 142-144.Zentralblatt MATH: 0078.01701
Mathematical Reviews (MathSciNet): MR95881
Project Euclid: euclid.ijm/1255380842 - J.-P. Serre, 1958 Modules projectifs et éspaces fibrés à fibre vectorielle, Séminaire Dubreil, Algèbre et théorie des nombres, Paris.
- M. Atiyah and F. Hirzebruch, 1959 Riemann-Roch theorems for differentiable manifolds, Bull. Amer. Math. Soc. 65, 276-281.Zentralblatt MATH: 0142.40901
Mathematical Reviews (MathSciNet): MR110106
Digital Object Identifier: doi:10.1090/S0002-9904-1959-10344-X
Project Euclid: euclid.bams/1183523205 - D. S. Rim, 1959 Modules over finite groups, Ann. of Math. 69, 700-712.Zentralblatt MATH: 0092.26104
Mathematical Reviews (MathSciNet): MR104721
Digital Object Identifier: doi:10.2307/1970033 - R. G. Swan, 1960 Induced representations and projective modules, Ann. of Math. 71, 552-578.Zentralblatt MATH: 0104.25102
Mathematical Reviews (MathSciNet): MR138688
Digital Object Identifier: doi:10.2307/1969944 - J. Milnor, 1961 Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. 74, 575-590.Zentralblatt MATH: 0102.38103
Mathematical Reviews (MathSciNet): MR133127
Digital Object Identifier: doi:10.2307/1970299 - D. S. Rim, 1961 On projective class groups, Trans. Amer. Math. Soc. 98, 459-467.Zentralblatt MATH: 0105.01401
Mathematical Reviews (MathSciNet): MR124378
Digital Object Identifier: doi:10.1090/S0002-9947-1961-0124378-1 - S. Smale, 1961 Generalized Poincaré's conjecture in dimensions greater than four, Ann. of Math. 74, 391-406.Zentralblatt MATH: 0099.39202
Mathematical Reviews (MathSciNet): MR137124
Digital Object Identifier: doi:10.2307/1970239 - A. H. Wallace, 1961 Modifications and cobounding manifolds. II, J. Math. Mech. 10, 773-809.
- J. F. Adams, 1962 Vector fields on spheres, Ann. of Math. 75, 603-632.Zentralblatt MATH: 0112.38102
Mathematical Reviews (MathSciNet): MR139178
Digital Object Identifier: doi:10.2307/1970213 - H. Bass and S. Schanuel, 1962 The homotopy theory of projective modules, Bull. Amer. Math. Soc. 68, 425-428.Zentralblatt MATH: 0108.26402
Mathematical Reviews (MathSciNet): MR152559
Digital Object Identifier: doi:10.1090/S0002-9904-1962-10826-X
Project Euclid: euclid.bams/1183524690 - A. Borel and Harish-Chandra, 1962 Arithmetic subgroups of algebraic groups, Ann. of Math. 75, 485-535.Zentralblatt MATH: 0107.14804
Mathematical Reviews (MathSciNet): MR147566
Digital Object Identifier: doi:10.2307/1970210 - J. Milnor, 1962 A duality theorem for Reidemeister torsion, Ann. of Math. 76, 137-147.Zentralblatt MATH: 0108.36502
Mathematical Reviews (MathSciNet): MR141115
Digital Object Identifier: doi:10.2307/1970268 - S. Smale, 1962 On the structure of manifolds, Amer. J. Math. 84, 387-399.Zentralblatt MATH: 0109.41103
Mathematical Reviews (MathSciNet): MR153022
Digital Object Identifier: doi:10.2307/2372978 - R. G. Swan, 1962 Vector bundles and projective modules, Trans. Amer. Math. Soc. 105, 264-277.Zentralblatt MATH: 0109.41601
Mathematical Reviews (MathSciNet): MR143225
Digital Object Identifier: doi:10.1090/S0002-9947-1962-0143225-6 - R. G. Swan, 1962 Projective modules over group rings and maximal orders, Ann. of Math. 76, 55-61.Zentralblatt MATH: 0112.02702
Mathematical Reviews (MathSciNet): MR139635
Digital Object Identifier: doi:10.2307/1970264 - D. Barden, 1963 The structure of manifolds, Ph. D. Thesis, Cambridge University, Cambridge, England
- B. Mazur, 1963 Relative neighborhoods and the theorems of Smale, Ann. of Math. 77, 232-249.Zentralblatt MATH: 0112.38301
Mathematical Reviews (MathSciNet): MR150786
Digital Object Identifier: doi:10.2307/1970215 - J. Milnor, 1963 Morse theory, Princeton Univ. Press, Princeton, N. J.
- J. Munkres, 1963 Elementary differential topology, Princeton Univ. Press, Princeton, N. J.
- H. Bass, 1964 The stable structure of quite general linear groups, Bull. Amer. Math. Soc. 70, 429-433.Zentralblatt MATH: 0232.20092
Mathematical Reviews (MathSciNet): MR160825
Digital Object Identifier: doi:10.1090/S0002-9904-1964-11130-7
Project Euclid: euclid.bams/1183526030 - H. Bass, 1964 K-theory and stable algebra, Publ. de l'Inst. des Hautes Etudes Sci. #22.Zentralblatt MATH: 0248.18025
Mathematical Reviews (MathSciNet): MR174604
Digital Object Identifier: doi:10.1007/BF02684689 - H. Bass, A. Heller and R. Swan, 1964 The Whitehead group of a polynomial extension, Publ. de l'Inst. des Hautes Etudes Sci. #22.Zentralblatt MATH: 0248.18026
Mathematical Reviews (MathSciNet): MR174605
Digital Object Identifier: doi:10.1007/BF02684690 - H. Bass, M. Lazard and J.-P. Serre, 1964 Sous-groupes d'indice fini dans SL(n, Z), Bull. Amer. Math. Soc. 70, 385-392.Zentralblatt MATH: 0232.20086
Mathematical Reviews (MathSciNet): MR161913
Digital Object Identifier: doi:10.1090/S0002-9904-1964-11107-1
Project Euclid: euclid.bams/1183526018 - J. Milnor, 1964 Some free actions of cyclic groups on spheres, Differential Analysis, Tata Institute and Oxford University Press, 37-42.
- G. Schrutka v. Rechtenstamm, 1964 Tabelle der (Relativ)-Klassenzahlen der Kreiskörper..., Abh. Deutsch. Akad. Wiss. Berlin, #2, 64 pp.
- G. de Rham 1964 (1), Reidemeister's torsion invariant and rotations of Sn, Differential Analysis, Tata Institute and Oxford Univ. Press, 27-36.
- G. de Rham 1964 (2), Torsion et type simple d'homotopy, Séminaire Math. Université de Lausanne. (Lectures by Kervaire, Maumary, and de Rham.)Zentralblatt MATH: 0153.53901
- J. Stallings 1964 Projective class groups and Whitehead groups, (mimeographed) Rice University, Houston, Texas.
- R. Szczarba 1964 On tangent bundles of fibre spaces and quotient spaces, Amer. J. Math. 86, 685-697.Zentralblatt MATH: 0151.31703
Mathematical Reviews (MathSciNet): MR172303
Digital Object Identifier: doi:10.2307/2373152 - C. T. C. Wall 1964 Differential topology, Part IV, Theory of handle decompositions (mimeographed), Cambridge University, Cambridge, England.
- J. Folkman 1965 Equivariant maps of spheres into the classical groups, Ph. D. Thesis, Princeton University, Princeton, N. J.
- S. Gersten 1965 (1), Whitehead groups of free associative algebras, Bull. Amer. Math. Soc. 71, 157-159.Zentralblatt MATH: 0234.16019
Mathematical Reviews (MathSciNet): MR169875
Digital Object Identifier: doi:10.1090/S0002-9904-1965-11268-X
Project Euclid: euclid.bams/1183526406 - S. Gersten 1965 (2), Ph. D. Thesis, Cambridge University, Cambridge.
- K. W. Kwun and R. H. Szczarba 1965 Product and sum theorems for Whitehead torsion, Ann. of Math. 82, 183-190.Zentralblatt MATH: 0142.40703
Mathematical Reviews (MathSciNet): MR182972
Digital Object Identifier: doi:10.2307/1970568 - J. L. Mennicke 1965 Finite factor groups of the unimodular group. Ann. of Math. 81, 31-37.Zentralblatt MATH: 0135.06504
Mathematical Reviews (MathSciNet): MR171856
Digital Object Identifier: doi:10.2307/1970380 - J. Milnor 1965 Lectures on the h-cobordism theorem, Notes by L. Siebenmann and J. Sondow, Princeton Univ. Press, Princeton, N. J.
- L. Siebenmann 1965 The obstruction to finding a boundary for an open manifold of dimension greater than five, Ph. D. Thesis, Princeton University, Princeton, N. J.
- J. Sondow 1965 Disproof of the Hauptvermutung for manifold pairs, Ph. D. Thesis, Princeton University, Princeton, N. J.
- J. Stallings 1965 (1), Whitehead torsion of free products, Ann. of Math. 82, 354-363.Zentralblatt MATH: 0132.26804
Mathematical Reviews (MathSciNet): MR179270
Digital Object Identifier: doi:10.2307/1970647 - J. Stallings 1965 (2), On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology, (A Symposium in honor of M. Morse), Princeton University Press, Princeton, N. J., 245-254.
- C. T. C. Wall 1965 Finiteness conditions for CW-complexes, Ann. of Math. 81, 56-69.Zentralblatt MATH: 0152.21902
Mathematical Reviews (MathSciNet): MR171284
Digital Object Identifier: doi:10.2307/1970382 - M. F. Atiyah and R. Bott 1966 A Lefschetz fixed point formula for elliptic differential operators, Bull. Amer. Math. Soc. 72, 245-250. To appear:Zentralblatt MATH: 0151.31801
Mathematical Reviews (MathSciNet): MR190950
Digital Object Identifier: doi:10.1090/S0002-9904-1966-11483-0
Project Euclid: euclid.bams/1183527784 - H, Bass The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups.Zentralblatt MATH: 0166.02401
- H. Bass and M. P. Murthy Grothendieck groups and Picard groups of abelian group rings.Zentralblatt MATH: 0157.08202
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