The Hauptvermutung[a] of geometric topology is a now refuted conjecture asking whether any two triangulations of a triangulable space have subdivisions that are combinatorially equivalent, i.e. the subdivided triangulations are built up in the same combinatorial pattern. It was originally formulated as a conjecture in 1908 by Ernst Steinitz[1] and Heinrich Franz Friedrich Tietze,[2] but it is now known to be false.
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^Steinitz, E. (1908). "Beiträge zur Analysis situs". Sitz-Ber. Berlin Math. Ges. 7: 29–49.
^Tietze, H. (1908). "Über die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten". Monatsh. Für Math. Und Phys. 19: 1–118. doi:10.1007/BF01736688. S2CID 120998023.
The Hauptvermutung of geometric topology is a now refuted conjecture asking whether any two triangulations of a triangulable space have subdivisions that...
since then gained wider acceptance, although doubts still remain. The Hauptvermutung (German for main conjecture) of geometric topology is the conjecture...
that continues to mature to this day. In 1961 Milnor disproved the Hauptvermutung by illustrating two simplicial complexes that are homeomorphic but combinatorially...
American Alma mater Harvard University (BA 2001; PhD 2004) Known for Hauptvermutung Seiberg–Witten Floer theory Awards E. H. Moore Prize (2019) EMS Prize...
Among other discoveries, he contributed to the disproof of the manifold Hauptvermutung, introduced the Casson invariant, a modern invariant for 3-manifolds...
"Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung". Annals of Mathematics. Second Series. 56 (1): 96–114. doi:10.2307/1969769...
classifying high-dimensional manifolds. His thesis work was focused on the Hauptvermutung. In an influential set of notes in 1970, Sullivan put forward the radical...
February 1964(1964-02-17) (aged 83) Munich, West Germany Known for Tietze's graph Tietze extension theorem Tietze transformations Hauptvermutung Lens space...
need not be unique—it can have infinitely many. This is elaborated at Hauptvermutung. The obstruction to placing a PL structure on a topological manifold...
; Armstrong, M.A.; Rourke, Colin P.; Cooke, G.E. (2013-03-09). The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds. Springer...
Größencharakter) Hauptmodul (the generator of a modular curve of genus 0) Hauptvermutung Hilbert's Nullstellensatz (without apostrophe in German) Ideal (originally...
'manifold-like'. A central conjecture of the causal set program, called the Hauptvermutung ('fundamental conjecture'), is that the same causal set cannot be faithfully...
Notes, Vol. 226, 227, Cambridge University Press, 1995. Editor: The Hauptvermutung Book, Kluwer, 1996. Editor with Sylvain Cappell and Jonathan Rosenberg:...
topology already appeared in the Alexandrov–Hopf book Topologie I (1935). Hauptvermutung Topological combinatorics Topological graph theory For example L'émergence...
Einschluss der Elemente der Topologie, by Hans Rademacher. Hall algebra Hauptvermutung Medial graph Steinitz class Steinitz exchange lemma Supernatural numbers...
to homotopy. Gysin sequence Hauptvermutung 1. Hauptvermutung, a German for main conjecture, is short for die Hauptvermutung der kombinatorischen Topologie...
general topology, the history of the classification theorem, and the Hauptvermutung (the theorem that every surface can be triangulated). This is a textbook...
Manolescu (known for his application of Seiberg–Witten Floer theory to the Hauptvermutung). Finally, strong research in mathematical analysis, complex analysis...
"Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung", Annals of Mathematics, Second Series, 56 (1): 96–114, doi:10.2307/1969769...
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