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Circle valued Morse theory and Novikov homology
Andrew Ranicki
An introduction to circle valued Morse theory and Novikov homology, from an algebraic point of view.
The structure set of an arbitrary space, the algebraic surgery exact sequence and the total surgery obstruction
Andrew Ranicki
An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.
Foundations of algebraic surgery
Andrew Ranicki
An elementary introduction to the principles of algebraic surgery.
Controlled surgery with trivial local fundamental groups
Erik Pedersen, Frank Quinn, Andrew Ranicki
We provide a proof of the controlled surgery sequence, including stability, in the special case that the local fundamental groups are trivial. Stability is a key ingredient in the…
Noncommutative localization and chain complexes I. Algebraic K- and L-theory
Amnon Neeman, Andrew Ranicki
The noncommutative (Cohn) localization S^{-1}R of a ring R is defined for any collection S of morphisms of f.g. projective left R-modules. We exhibit S^{-1}R as the endomorphism ri…
Rigidity and gluing for Morse and Novikov complexes
Octav Cornea, Andrew Ranicki
We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result…