Geometric diffeomorphism finiteness in low dimensions and homotopy group finiteness
نویسندگان
چکیده
منابع مشابه
Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness
Our main result asserts that for any given numbers C and D the class of simply connected closed smooth manifolds of dimension m < 7 which admit a Riemannian metric with sectional curvature bounded in absolute value by |K| ≤ C and diameter uniformly bounded from above by D contains only finitely many diffeomorphism types. Thus in these dimensions the lower positive bound on volume in Cheeger’s F...
متن کاملThe Geometric Finiteness Obstruction
The purpose of this paper is to develop a geometric approach to Wall's finiteness obstruction. We will do this for equivariant CW-complexes. The main advantage will be that we can derive all the formal properties of the equivariant finiteness obstruction easily from this geometric description. Namely, the obstruction property, homotopy invariance, the sum and product formulas, and the restricti...
متن کاملDIFFEOMORPHISM FINITENESS, POSITIVE PINCHING, AND SECOND HOMOTOPY A. Petrunin and W. Tuschmann
Our main results can be stated as follows: 1. For any given numbers m, C and D, the class of m-dimensional simply connected closed smooth manifolds with finite second homotopy groups which admit a Riemannian metric with sectional curvature bounded in absolute value by |K| ≤ C and diameter uniformly bounded from above by D contains only finitely many diffeomorphism types. 2. Given any m and any ...
متن کاملSpectral Sequence Notes: Finiteness of homotopy groups
X Assume that X is locally finite, and let i ≥ 2 be the first dimension in which X has non-zero reduced homology. Then ΩX is i− 2 connected and Hi−1(ΩX) = πi−1(ΩX) = πi(X) = Hi(X) by using the Hurewicz theorem together with the shift in homotopy corresponding to Ω. So Hi−1(ΩX) is finitely generated. We will do induction, and this serves as our base space. [You might be worried about the case i ...
متن کاملGeometric Finiteness in Negatively Pinched Hadamard Manifolds
In this paper, we generalize Bonahon’s characterization of geometrically infinite torsion-free discrete subgroups of PSL(2,C) to geometrically infinite discrete torsionfree subgroups Γ of isometries of negatively pinched Hadamard manifolds X. We then generalize a theorem of Bishop to prove that every such geometrically infinite isometry subgroup Γ has a set of nonconical limit points with cardi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2002
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s002080100281