Hauptvermutung

The Hauptvermutung is the conjecture that any two triangulations of a polyhedron (such as a combinatorial manifold) are combinatorially equivalent.
  • Ueber die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten by H. Tietze,
    Monatshefte fuer Math. und Phys. 19, 1-118 (1908)
  • Beitraege zur Analysis situs by E. Steinitz, Sitz.-Ber. Berl. Math. Ges. 7, 29-49 (1908)
  • Die Topologie der Mannigfaltigkeiten by H. Kneser, Jahresb. D.M.V. 34, 1-13 (1926)
  • Page 152 of Topologie by P. Alexandroff and H. Hopf, Springer (1935)
  • Two complexes which are homeomorphic but combinatorially distinct by J. Milnor, Ann. of Math. 74, 575--590 (1961)
  • On the Hauptvermutung for manifolds, by D.Sullivan, Bull. A.M.S. 73, 598--600 (1967)
  • On the triangulation of manifolds and the Hauptvermutung by R.Kirby and L.Siebenmann, Bull. A.M.S. 75, 742--749 (1968)
  • Topological Manifolds by L.Siebenmann, Proc. 1970 Nice ICM, Gauthier--Villars, Vol. 2, 133--163 (1971)
  • Some Recent Results on Topological Manifolds by R.Schultz, American Mathematical Monthly 78, 941--952 (1971)
  • Geometric periodicity and the invariants of manifolds by D.Sullivan, in Manifolds--Amsterdam 1970 (Proc. Nuffic Summer School)
    Springer Lecture Notes in Mathematics, Vol. 197, 44--75 (1971)
  • Foundational Essays on Topological Manifolds, Smoothings, and Triangulations by R.Kirby and L.Siebenmann,
    Annals of Mathematics Studies 88, Princeton (1976). MR review.
    Maybe I'm doin' it wrong (MP3 file) Randy Newman song referred to on page 283. Lyrics.
  • Hauptvermutung by H.Samelson, American Mathematical Monthly 85, 567--569 (1978)
  • A geometric interpretation of Siebenmann's periodicity phenomenon by S.Cappell and S.Weinberger,
    Geometry and topology, Lecture Notes in Pure and Appl. Math. 105, 47--52, Dekker (1985)
  • Algebraic L-theory and topological manifolds by A.Ranicki, Cambridge Tracts in Mathematics 102, CUP (1992)
  • Epsilon surgery by S.Ferry and E.K.Pedersen, Proc. 1993 Oberwolfach conference on the Novikov conjecture, Vol. 2,
    LMS Lecture Notes 227, CUP, 167--226 (1995)
    Section 13 is particularly relevant.
  • The Hauptvermutung Book (edited by A.R.) K-Monographs in Mathematics 1, Springer (ex-Kluwer) (1996)
    Mathematical Reviews review Zentralblatt review
    Individual papers:
    On the Hauptvermutung by A.Ranicki (1996)
    Generalisations and Applications of Block Bundles by A.Casson (1967)
    Triangulating Homotopy Equivalences and Homeomorphisms by D.Sullivan (1967)
    The Princeton Notes on the Hauptvermutung by M.Armstrong, G.Cooke and C.Rourke (1968)
  • Some history of the Hauptvermutng (F.Quinn and A.R.) Leter to the Editor, Mathematical Intelligencer 19 (4), 5 (1997)
  • On Siebenmann periodicity by S.Hutt, Pacific J. Math. 183, 291--303 (1998)
  • Classical and Modern Topology by S.P. Novikov (2000). MR review.
  • Piecewise linear structures on topological manifolds by Y. Rudyak (2001)
  • Fragments of geometric topology from the sixties. by S. Buoncristiano, Geometry and Topology Monographs 6 (2003)
  • High dimensional manifold topology then and now Slides of 3 lectures by A.Ranicki at Siebenmann conference, Orsay (2005)
  • Oberwolfach Mini-Workshop on the Hauptvermutung for High-Dimensional Manifolds 13-19 August, 2006. Photo Report
  • A controlled-topology proof of the product structure theorem by F.Quinn, e-print GT/061031
  • Google for the Hauptvermutung