Rigidity of the Álvarez class

Nozawa, Hiraku

doi:10.1007/s00229-010-0347-3

Cited by 8 publications

(21 citation statements)

References 16 publications

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“…9 in Nozawa [11] shown there. The commutativity of the diagram (12) follows from the commutativity of the diagram (7) in Nozawa [11]. In fact, the commutativity of the diagram implies that…”

Section: The First Projection and A Is Given By The Homomor-mentioning

confidence: 85%

“…This is clearly a homomorphism. As shown in Nozawa [11], f G depends only on the isotopy class of f .…”

Section: The First Projection and A Is Given By The Homomor-mentioning

confidence: 95%

“…Proof We recall the definition of a homomorphism : π 0 (Diff(F, x 0 , F | F )) −→ Aut G defined in Nozawa [11]. Since the leaves of (F, F | F ) are dense, the Lie algebra of transverse fields…”

Section: The First Projection and A Is Given By The Homomor-mentioning

confidence: 99%

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Minimizability of developable Riemannian foliations

Nozawa

2010

Ann Glob Anal Geom

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Let (M,F) be a closed manifold with a Riemannian foliation. We show that the secondary characteristic classes of the Molino's commuting sheaf of (M,F) vanish if (M,F) is developable and the fundamental group of M is of polynomial growth. By theorems of \'{A}lvarez L\'{o}pez, our result implies that (M,F) is minimizable under the same conditions. As a corollary, we show that (M,F) is minimizable if F is of codimension 2 and the fundamental group of M is of polynomial growth.Comment: 15 pages, correction of misprint

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Section: The First Projection and A Is Given By The Homomor-mentioning

confidence: 85%

“…This is clearly a homomorphism. As shown in Nozawa [11], f G depends only on the isotopy class of f .…”

Section: The First Projection and A Is Given By The Homomor-mentioning

confidence: 95%

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Minimizability of developable Riemannian foliations

Nozawa

2010

Ann Glob Anal Geom

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“…Thus, the operator * maps ∆ θ -harmonic forms to ∆ κ b −θ -harmonic forms and vice versa, so from the basic Hodge theorem for basic Lichnerowicz cohomology (see [15,Section 3.3]), * induces the required isomorphism. It has been shown previously by H. Nozawa in [19], [20] that theÁlvarez class [κ b ] is continuous with respect to smooth deformations of Riemannian foliations. The following proposition extends these results further.…”

Section: 2mentioning

confidence: 99%

Homotopy invariance of cohomology and signature of a Riemannian foliation

Habib

Richardson

2018

Math. Z.

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We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant. We also show that foliated homotopic maps between Riemannian foliations induce isomorphic maps on basic Lichnerowicz cohomology, and that thé Alvarez class of a Riemannian foliation is invariant under foliated homotopy equivalence.2010 Mathematics Subject Classification. 53C12; 53C21; 58J50; 58J60.

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“…The Molino's commuting sheaf C of (M, F) is determined by the structure group as follows (we refer TOME 64 (2014), FASCICULE 4 to [22,Section 5.3] for the definition of the Molino's commuting sheaf). The following proposition is a direct consequence of [24,Proposition 6]:…”

Section: Molino's Commuting Sheaf Of Linearly Foliated Torus Bundlesmentioning

confidence: 99%