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A counterexample to questions on the integrality property of virtual signature

✍ Scribed by Ranja Roy

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 96 KB
Volume: 100
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00087-x

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✦ Synopsis

Wall (1961)
, defined the virtual Euler Characteristic χ(Γ ) of an arbitrary group Γ of finite homological type as χ(Γ ) = χ(Γ )/[Γ : Γ ] ∈ Q, where Γ is any torsion free subgroup of finite index in Γ . Analogous to virtual Euler Characteristic, we define the Virtual signature of an oriented virtual Poincare Duality group, a rational number. We show that two of Ken Brown's results on questions regarding the integrality property of virtual Euler Characteristics when formulated in the Virtual signature case is false.

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