Geometric Chain Homotopy Equivalences Between Novikov Complexes

Schütz, Dirk

doi:10.1142/9789812704443_0021

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2007

2024

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“…This is a chain complex which is finitely generated free over ZG ξ , where G is a quotient of π 1 (M) by a normal subgroup contained in ker ξ . For details on several constructions, we refer the reader to Novikov [15], Latour [12], Pajitnov [17], Farber [6] or Schütz [25]. It turns out that its chain homotopy type is that of C * (M; ZG ξ ).…”

Section: Introductionmentioning

confidence: 99%

On the Whitehead group of Novikov rings associated to irrational homomorphisms

Schütz

2007

Journal of Pure and Applied Algebra

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Given a homomorphism ξ : G → R we show that the natural map i * : Wh(G) → Wh(G; ξ ) from the Whitehead group of G to the Whitehead group of the Novikov ring is surjective. The group Wh(G; ξ ) is of interest for the simple chain homotopy type of the Novikov complex. It also contains the Latour obstruction for the existence of a nonsingular closed 1-form within a fixed cohomology class ξ ∈ H 1 (M; R), where M is a closed connected smooth manifold.

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