Inventiones mathematicae

, Volume 189, Issue 2, pp 315–357 | Cite as

A notion of geometric complexity and its application to topological rigidity

  • Erik Guentner
  • Romain TesseraEmail author
  • Guoliang Yu


We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is homotopy equivalent to M, then M×ℝ n is homeomorphic to N×ℝ n , for n large enough. This statement is known as the stable Borel conjecture. On the other hand, we show that the class of FDC groups includes all countable subgroups of GL(n,K), for any field K.


Manifold Fundamental Group Geometric Complexity Decomposition Complexity Whitehead Group 
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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Hawai‘i at MānoaHonoluluUSA
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA
  3. 3.UMPAENS de LyonLyon Cedex 07France

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