scholarly journals Density of smooth maps for fractional Sobolev spaces W s,p into ℓ simply connected manifolds when s≥1

10.5802/cml.5 ◽  
2017 ◽  
Vol 5 (2) ◽  
pp. 3-24 ◽  
Author(s):  
Pierre Bousquet ◽  
Augusto C. Ponce ◽  
Jean Van Schaftingen
Keyword(s):  
Sobolev Spaces ◽  
Fractional Sobolev Spaces ◽  
Smooth Maps ◽  
Simply Connected Manifolds ◽  
Simply Connected

scholarly journals TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP

2021 ◽  
pp. 1-8
Author(s):  
DANIEL KASPROWSKI ◽  
MARKUS LAND
Keyword(s):  
Fundamental Group ◽  
Homotopy Equivalent ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Canonical Map ◽  
Duality Space ◽  
Simply Connected Manifolds ◽  
Simply Connected ◽  
Poincaré Duality Space

Abstract Let $\pi$ be a group satisfying the Farrell–Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$ has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby–Siebenmann invariant. If $\pi$ is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby–Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel’s conjecture, and simply connected manifolds where rigidity is a consequence of Freedman’s classification results.

scholarly journals Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds

1998 ◽  
Vol 28 (2) ◽  
pp. 207-212 ◽  
Author(s):  
Ichiji Kurazono ◽  
Takao Matumoto
Keyword(s):  
Connected Sum ◽  
Simply Connected Manifolds ◽  
Simply Connected

scholarly journals Composition in fractional Sobolev spaces

2001 ◽  
Vol 7 (2) ◽  
pp. 241-246 ◽  
Author(s):  
Haim Brezis ◽  
◽  
Petru Mironescu ◽  
Keyword(s):  
Sobolev Spaces ◽  
Fractional Sobolev Spaces

Generalized Gagliardo–Nirenberg inequalities using Lorentz spaces, BMO, Hölder spaces and fractional Sobolev spaces

2018 ◽  
Vol 173 ◽  
pp. 146-153 ◽  
Author(s):  
Nguyen Anh Dao ◽  
Jesus Ildefonso Díaz ◽  
Quoc-Hung Nguyen
Keyword(s):  
Sobolev Spaces ◽  
Lorentz Spaces ◽  
Fractional Sobolev Spaces ◽  
Hölder Spaces ◽  
Holder Spaces

scholarly journals A distributional approach to fractional Sobolev spaces and fractional variation: Existence of blow-up

2019 ◽  
Vol 277 (10) ◽  
pp. 3373-3435 ◽  
Author(s):  
Giovanni E. Comi ◽  
Giorgio Stefani
Keyword(s):  
Sobolev Spaces ◽  
Blow Up ◽  
Fractional Sobolev Spaces

A density result for fractional Sobolev spaces

2016 ◽  
pp. 43-62
Author(s):  
Giovanni Molica Bisci ◽  
Vicentiu D. Radulescu ◽  
Raffaella Servadei
Keyword(s):  
Sobolev Spaces ◽  
Fractional Sobolev Spaces ◽  
Density Result

A Cohomological Criterion for Density of Smooth Maps in Sobolev Spaces Between Two Manifolds

Nematics ◽  
1991 ◽  
pp. 15-23 ◽  
Author(s):  
F. Bethuel ◽  
J. M. Coron ◽  
F. Demengel ◽  
F. Helein
Keyword(s):  
Sobolev Spaces ◽  
Smooth Maps
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