Whitehead torsion
HTML articles powered by AMS MathViewer
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 29, 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.
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.
- Georges de Rham, Sur les complexes avec automorphismes, Comment. Math. Helv. 12 (1940), 191–211 (French). MR 2551, DOI 10.1007/BF01620647 J. H. C. Whitehead, 1939 Simplicial spaces, nuclei and m-groups, Proc. London Math. Soc. 45, 243-327.
- Graham. Higman, The units of group-rings, Proc. London Math. Soc. (2) 46 (1940), 231–248. MR 2137, DOI 10.1112/plms/s2-46.1.231
- J. H. C. Whitehead, On $C^1$-complexes, Ann. of Math. (2) 41 (1940), 809–824. MR 2545, DOI 10.2307/1968861
- J. H. C. Whitehead, On incidence matrices, nuclei and homotopy types, Ann. of Math. (2) 42 (1941), 1197–1239. MR 5352, DOI 10.2307/1970465
- Jean Dieudonné, Les déterminants sur un corps non commutatif, Bull. Soc. Math. France 71 (1943), 27–45 (French). MR 12273, DOI 10.24033/bsmf.1345
- Carl Ludwig Siegel, Discontinuous groups, Ann. of Math. (2) 44 (1943), 674–689. MR 9959, DOI 10.2307/1969104
- J. H. C. Whitehead, Combinatorial homotopy. I, Bull. Amer. Math. Soc. 55 (1949), 213–245. MR 30759, DOI 10.1090/S0002-9904-1949-09175-9
- Kurt Reidemeister, Complexes and homotopy chains, Bull. Amer. Math. Soc. 56 (1950), 297–307. MR 36506, DOI 10.1090/S0002-9904-1950-09404-X
- G. de Rham, Complexes à automorphismes et homéomorphie différentiable, Ann. Inst. Fourier (Grenoble) 2 (1950), 51–67 (1951) (French). MR 43468, DOI 10.5802/aif.19
- J. H. C. Whitehead, Simple homotopy types, Amer. J. Math. 72 (1950), 1–57. MR 35437, DOI 10.2307/2372133
- Helmut Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952 (German). MR 0049239
- Irving Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc. 72 (1952), 327–340. MR 46349, DOI 10.1090/S0002-9947-1952-0046349-0
- Paul Olum, Mappings of manifolds and the notion of degree, Ann. of Math. (2) 58 (1953), 458–480. MR 58212, DOI 10.2307/1969748
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
- Irving Reiner, Normal subgroups of the unimodular group, Illinois J. Math. 2 (1958), 142–144. MR 95881
- J.-P. Serre, Modules projectifs et espaces fibrés à fibre vectorielle, Séminaire P. Dubreil, M.-L. Dubreil-Jacotin et C. Pisot, 1957/58, Fasc. 2, Exposé 23, Secrétariat mathématique, Paris, 1958, pp. 18 (French). MR 0177011
- M. F. Atiyah and F. Hirzebruch, Riemann-Roch theorems for differentiable manifolds, Bull. Amer. Math. Soc. 65 (1959), 276–281. MR 110106, DOI 10.1090/S0002-9904-1959-10344-X
- Dock Sang Rim, Modules over finite groups, Ann. of Math. (2) 69 (1959), 700–712. MR 104721, DOI 10.2307/1970033
- Richard G. Swan, Induced representations and projective modules, Ann. of Math. (2) 71 (1960), 552–578. MR 138688, DOI 10.2307/1969944
- John Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. (2) 74 (1961), 575–590. MR 133127, DOI 10.2307/1970299
- Dock Sang Rim, On projective class groups, Trans. Amer. Math. Soc. 98 (1961), 459–467. MR 124378, DOI 10.1090/S0002-9947-1961-0124378-1
- Stephen Smale, Generalized Poincaré’s conjecture in dimensions greater than four, Ann. of Math. (2) 74 (1961), 391–406. MR 137124, DOI 10.2307/1970239
- Andrew H. Wallace, Modifications and cobounding manifolds. II, J. Math. Mech. 10 (1961), 773–809. MR 0130695
- J. F. Adams, Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603–632. MR 139178, DOI 10.2307/1970213
- H. Bass and S. Schanuel, The homotopy theory of projective modules, Bull. Amer. Math. Soc. 68 (1962), 425–428. MR 152559, DOI 10.1090/S0002-9904-1962-10826-X
- Armand Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485–535. MR 147566, DOI 10.2307/1970210
- John Milnor, A duality theorem for Reidemeister torsion, Ann. of Math. (2) 76 (1962), 137–147. MR 141115, DOI 10.2307/1970268
- S. Smale, On the structure of manifolds, Amer. J. Math. 84 (1962), 387–399. MR 153022, DOI 10.2307/2372978
- Richard G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (1962), 264–277. MR 143225, DOI 10.1090/S0002-9947-1962-0143225-6
- Richard G. Swan, Projective modules over group rings and maximal orders, Ann. of Math. (2) 76 (1962), 55–61. MR 139635, DOI 10.2307/1970264 D. Barden, 1963 The structure of manifolds, Ph. D. Thesis, Cambridge University, Cambridge, England
- Barry Mazur, Relative neighborhoods and the theorems of Smale, Ann. of Math. (2) 77 (1963), 232–249. MR 150786, DOI 10.2307/1970215
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331, DOI 10.1515/9781400881802
- James R. Munkres, Elementary differential topology, Annals of Mathematics Studies, No. 54, Princeton University Press, Princeton, N.J., 1963. Lectures given at Massachusetts Institute of Technology, Fall, 1961. MR 0163320, DOI 10.1515/9781400882656
- Hyman Bass, The stable structure of quite general linear groups, Bull. Amer. Math. Soc. 70 (1964), 429–433. MR 160825, DOI 10.1090/S0002-9904-1964-11130-7
- H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 5–60. MR 174604, DOI 10.1007/BF02684689
- H. Bass, A. Heller, and R. G. Swan, The Whitehead group of a polynomial extension, Inst. Hautes Études Sci. Publ. Math. 22 (1964), 61–79. MR 174605, DOI 10.1007/BF02684690
- H. Bass, M. Lazard, and J.-P. Serre, Sous-groupes d’indice fini dans $\textbf {SL}(n,\,\textbf {Z})$, Bull. Amer. Math. Soc. 70 (1964), 385–392 (French). MR 161913, DOI 10.1090/S0002-9904-1964-11107-1
- J. Milnor, Some free actions of cyclic groups on spheres, Differential Analysis, Bombay Colloq., 1964, Oxford Univ. Press, London, 1964, pp. 37–42. MR 0189055
- Guntram Schrutka von Rechtenstamm, Tabelle der (Relativ)-Klassenzahlen der Kreiskörper, deren $\varphi$-Funktion des Wurzelexponenten (Grad) nicht grösser als 256 ist, Abh. Deutsch. Akad. Wiss. Berlin Kl. Math. Phys. Tech. 1964 (1964), no. 2, 64 (German). MR 167646
- G. de Rham, Reidemeister’s torsion invariant and rotations of $S^n$, Differential Analysis, Bombay Colloq., 1964, Oxford Univ. Press, London, 1964, pp. 27–36. MR 0190945 G. de Rham 1964 (2), Torsion et type simple d’homotopy, Séminaire Math. Université de Lausanne. (Lectures by Kervaire, Maumary, and de Rham.) J. Stallings 1964 Projective class groups and Whitehead groups, (mimeographed) Rice University, Houston, Texas.
- R. H. Szczarba, On tangent bundles of fibre spaces and quotient spaces, Amer. J. Math. 86 (1964), 685–697. MR 172303, 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.
- Stephen Gersten, Whitehead groups of free associative algebras, Bull. Amer. Math. Soc. 71 (1965), 157–159. MR 169875, DOI 10.1090/S0002-9904-1965-11268-X S. Gersten 1965 (2), Ph. D. Thesis, Cambridge University, Cambridge.
- Kyung Whan Kwun and R. H. Szczarba, Product and sum theorems for Whitehead torsion, Ann. of Math. (2) 82 (1965), 183–190. MR 182972, DOI 10.2307/1970568
- Jens L. Mennicke, Finite factor groups of the unimodular group, Ann. of Math. (2) 81 (1965), 31–37. MR 171856, DOI 10.2307/1970380
- John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942, DOI 10.1515/9781400878055
- John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942, DOI 10.1515/9781400878055
- John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942, DOI 10.1515/9781400878055
- John Stallings, Whitehead torsion of free products, Ann. of Math. (2) 82 (1965), 354–363. MR 179270, DOI 10.2307/1970647
- John R. Stallings, On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 245–254. MR 0180983
- C. T. C. Wall, Finiteness conditions for $\textrm {CW}$-complexes, Ann. of Math. (2) 81 (1965), 56–69. MR 171284, DOI 10.2307/1970382
- M. F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic differential operators, Bull. Amer. Math. Soc. 72 (1966), 245–250. MR 190950, DOI 10.1090/S0002-9904-1966-11483-0 H, Bass The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups. H. Bass and M. P. Murthy Grothendieck groups and Picard groups of abelian group rings.
Additional Information
- Journal: Bull. Amer. Math. Soc. 72 (1966), 358-426
- DOI: https://doi.org/10.1090/S0002-9904-1966-11484-2
- MathSciNet review: 0196736