By F. Thomas Farrell

ISBN-10: 3540589775

ISBN-13: 9783540589778

This ebook is an creation to the topological tension theorem for compact non-positively curved Riemannian manifolds. It incorporates a quickly casual account of the heritage fabric from surgical procedure concept and regulated topology prerequesite to this consequence. it really is meant for researchers and complex graduate scholars in either differential geometry and topology. This publication is the content material of a path given through the writer at TIFR in 1993.

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**Extra resources for Surgical Methods in Rigidity (Tata Institute Lectures on Mathematics and Physics)**

**Example text**

3. Idg(v) I ::; 41vl for each vector v tangent to Tn. A new geometric group G1 on Tn is constructed by applying 9 to the basis elements of j*G. This process also yields a new automorphism 1. It It : G 1 -+ G1 such that is a 4,",{-automorphism, and Assuming 4'"'{ ::; 1, we can form the square matrix 11 with entries from Z(1rITn). 3 to do this, then 11 can be regarded as an automorphism of the "geometric group" p*G I over R. n , where p: R. n /(3Zt is the canonical projection. Considered this way, p*G1 is a free but not finitely generated Z-module.

Note that E x I F -t id AixI ' M be the W-bundle M is the (£1 x I) x 1-t E x I covering id M. Let 0+ W, 0_ W, 00 W be the parts of W lying over 0+ W, 0_ W, 00 W , bundle associated to -t M. Hence id Ai x -t F_ = W induces a bundle map G : V = 0+ W u 00 W respectively. These are r -invariant subspaces of oW and oW Denote the total spaces of associated su1;>bundles by 0+ V, can identify Gla_v: O_V -t observe that Glaov : 00 V -t 00 V, E x 0 with idE, and Gla+v: o+V 0_ V, respectively. We -t Ex 1 with ki E .

Then there exists d > 0 such that I : G -t G 01 a geometric group Proof. Let n = dim X and c: j represents 0 in Whr lor any d -automorphism G on X. = do/6n. 3 relative to c:. olnH where each Ii is c:-blocked. Note that each Ii is a do/6n-automorphism of G. 2 states that each represents 0 in Whr. And equation (1) implies that the element in W hr represented by I is the sum of the elements represented by Ii. D. It is useful to extend the construction I and the results about it to the case of d- isomorphisms.

### Surgical Methods in Rigidity (Tata Institute Lectures on Mathematics and Physics) by F. Thomas Farrell

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