Extension dimension and quasi-finite CW-complexes
نویسندگان
چکیده
منابع مشابه
1 1 M ay 2 00 4 EXTENSION DIMENSION AND QUASI - FINITE CW - COMPLEXES
We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications. Several results related to the class of quasi-finite complexes are established, such as completion of metrizable spaces, existence of universal spaces and a ve...
متن کاملL-invariants of Finite Aspherical Cw-complexes
Let X be a finite aspherical CW-complex whose fundamental group π1(X) possesses a subnormal series π1(X) ⊲ Gm ⊲ . . . ⊲ G0 with a non-trivial elementary amenable group G0. We investigate the L2-invariants of the universal covering of such a CW-complex X. We show that the NovikovShubin invariants αn(X̃) are positive. We further prove that the L2-torsion ρ(2)(X̃) vanishes if π1(X) has semi-integral...
متن کاملOn Complexes of Finite Complete Intersection Dimension
We study complexes of finite complete intersection dimension in the derived category of a local ring. Given such a complex of complexity c, we prove that the thick subcategory it generates contains complexes of all possible complexities at most c. In particular, we show that such a complex is virtually small, answering a question raised by Dwyer, Greenlees and Iyengar.
متن کاملAlgebraic Properties of Quasi-finite Complexes
A countable CW complexK is quasi-finite (as defined by A.Karasev [30]) if for every finite subcomplex M of K there is a finite subcomplex e(M) containing M such that any map f : A → M , A closed in a separable metric space X satisfying XτK, there is an extension g : X → e(M) of f . Levin’s [36] results imply that none of the Eilenberg-MacLane spaces K(G, 2) is quasi-finite if G = 0. In this pap...
متن کاملCW - complexes Stephen
The term CW-complex comes from “closure-finite with the weak topology”, where “closure-finite” refers to A3 and “weak topology” refers to A4. A finite complex is a CW-complex with only finitely many cells. Observe that if X is a finite complex, A4 is redundant, since W is the union of the compact sets φα((φ n α) −1W ), and these are closed since X is Hausdorff. If X has cells of dimension n but...
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: Topology and its Applications
سال: 2006
ISSN: 0166-8641
DOI: 10.1016/j.topol.2005.08.014