• Home
  • Algebraic Geometry
  • Download Novikov Conjectures, Index Theorems, and Rigidity by Steven C. Ferry, Andrew Ranicki, Jonathan M. Rosenberg PDF

Download Novikov Conjectures, Index Theorems, and Rigidity by Steven C. Ferry, Andrew Ranicki, Jonathan M. Rosenberg PDF

By Steven C. Ferry, Andrew Ranicki, Jonathan M. Rosenberg

The Novikov Conjecture is the one most vital unsolved challenge within the topology of high-dimensional non-simply hooked up manifolds. those volumes are the outgrowth of a convention held on the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September, 1993, as regards to `Novikov Conjectures, Index Theorems and Rigidity'. they're meant to provide a picture of the prestige of labor at the Novikov Conjecture and comparable issues from many issues of view: geometric topology, homotopy thought, algebra, geometry, research.

Show description

Read or Download Novikov Conjectures, Index Theorems, and Rigidity PDF

Best algebraic geometry books

The Novikov Conjecture: Geometry And Algebra

Those lecture notes comprise a guided travel to the Novikov Conjecture and comparable conjectures as a result of Baum-Connes, Borel and Farrell-Jones. they start with fundamentals approximately greater signatures, Whitehead torsion and the s-Cobordism Theorem. Then an advent to surgical procedure idea and a model of the meeting map is gifted.

Arithmetic Algebraic Geometry

This quantity comprises 3 lengthy lecture sequence by means of J. L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their issues are respectively the relationship among algebraic K-theory and the torsion algebraic cycles on an algebraic type, a brand new method of Iwasawa idea for Hasse-Weil L-function, and the functions of arithemetic geometry to Diophantine approximation.

Knots: Mathematics with a Twist

Knot concept is one quarter of arithmetic that has an important variety of functions. the particular performance of many organic molecules is derived mostly incidentally they twist and fold once they are created. through the years, loads of arithmetic has been invented to explain and examine knots.

Additional info for Novikov Conjectures, Index Theorems, and Rigidity

Sample text

The homotopy inverse limit holimF | C is now the product x∈C Ex , and the Γ–action is given ←− C by the equation γ · {ex } = {Fγ eγ −1 x }. Let A denote the set of orbits of the Γ–action on the objects of C, and let C α denote the subcategory on objects belonging to the orbit α. Then the above description shows that ∼ holim F | C −→ α∈A holim F | C α , and the isomorphism is equivariant, so ←− C ←− Cα it suffices to deal with the case where the Γ–action is transitive on the objects of C. In this case, holim F | C is Γ–isomorphic to the Γ–space γ∈Γ Xe , with ←− C Γ acting by permuting factors, and this space is in turn Γ–isomorphic to the space of functions F (Γ, Xe ).

We have shown that b Cˆ∗ (X; G) = Cˆ∗Ur (X; G) ⊆ Cˆ∗ (X; G) . r ˆ If we can show that each inclusion Cˆ∗Ur (X; G) → C(X; G) induces an isomorphism on homology, then the result will follow. 11. We write ∞ X = i=0 Xi , where each Xi is a metric space for which d takes only finite values, and in which all closed balls are compact. For each i, fix a point n xi ∈ Xi . 11. This gives the result. D. One now defines the analogous theory b h f (−, A), for A any spectrum, to be the realization of the simplicial spectrum k → lim h f (A; A).

K, k+1}. (Ns ×Σn ) Ψ can be written as lim k (Ns (k)× → Ns (k) Ψ Σn Pn , n s Σn ) Ψn . But (N (k) × Σn ) Ψn has nerve equivalent to since both have nerves weakly equivalent to E Σn ×Σn Ψ({k, k+1}) , as one easily checks using the hypothesis that Ψ({i, i + 1} → {i}) induces an equivalence on nerves for all i. D. We finally need to examine group actions on inverse limits. Let C be a category with an action by group Γ. We may view this action as a functor Γ → CAT , where Γ denotes Γ viewed as a category with one object.

Download PDF sample

Rated 4.00 of 5 – based on 15 votes