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Now showing items 1-10 of 21

#### Rigidity and gluing for Morse and Novikov complexes

(Final version, accepted for publication by the Journal of the European Mathematical Society, 2003-05-12)

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 is also proved for the Floer complex of a ...

#### CONTROLLED SURGERY WITH TRIVIAL LOCAL FUNDAMENTAL GROUPS

(2001-11-27)

We provide a proof of the controlled surgery sequence, including stabil-
ity, in the special case that the local fundamental groups are trivial. Stability is a
key ingredient in the construction of exotic homology manifolds ...

#### Circle valued Morse theory and Novikov homology

(Notes of lecture given at the Summer School on High-dimensional Manifold Topology, ICTP Trieste, May-June 2001. To appear in Vol. 1 of the Proceedings, 2001-11-30)

An introduction to circle valued Morse theory and Novikov homology, from an algebraic point of view.

#### Foundations of algebraic surgery

(Notes of lecture given at the Summer School on High-dimensional Manifold Topology, ICTP Trieste, May-June 2001. To appear in Vol. 1 of the Proceedings, 2001-11-30)

An elementary introduction to the principles of algebraic surgery.

#### Blanchfield and Seifert algebra in high dimensional knot theory

(2003-01-13)

Novikov initiated the study of the algebraic properties of quadratic forms over polynomial extensions by a far-reaching analogue of the Pontrjagin-Thom transversality construction of a Seifert surface of a knot and the ...

#### Noncommutative localization in topology

(To appear in the Proceedings of the Conference on Noncommutative Localization in Algebra and Topology, ICMS, Edinburgh, 29-30 April, 2002, 2003-08-14)

The topological applications of the Cohn noncommutative localization considered
in this paper deal with spaces (especially manifolds) with infinite
fundamental group, and involve localizations of infinite group rings ...

#### The structure set of an arbitrary space, the algebraic surgery exact sequence and the total surgery obstruction

(Notes of lecture given at the Summer School on High-dimensional Manifold Topology, ICTP Trieste, May-June 2001. To appear in Vol. 1 of the Proceedings, 2001-11-30)

The algebraic theory of surgery gives a necessary and suffcient chain level condition
for a space with n-dimensional Poincare duality to be homotopy equivalent to an n-
dimensional topological manifold. A relative version ...

#### REPRESENTATIONS OF ALGEBRAS AS UNIVERSAL LOCALIZATIONS

(to appear in the Mathematical Proceedings of the Cambridge Philosophical Society, 2002-05-03)

Given a presentation of a finitely presented group, there is a natural way to
represent the group as the fundamental group of a 2-complex. The first part
of this paper demonstrates one possible way to represent a finitely ...

#### Generalized Arf invariants in algebraic L-theory

(2003-04-23)

The difference between the quadratic L-groups L.(A) and the sym-
metric L-groups L*(A) of a ring with involution A is detected by generalized Arf
invariants. The special case A = Z[x] gives a complete set of invariants ...

#### THE WHITEHEAD GROUP OF THE NOVIKOV RING

(http://arxiv.org/pdf/math.AT/0012031, 2000)

The Bass-Heller-Swan-Farrell-Hsiang-Siebenmann decomposition of the Whitehead group $K_1(A_{\rho}[z,z^{-1}])$ of a twisted Laurent polynomial extension $A_{\rho}[z,z^{-1}]$ of a ring $A$ is generalized to a decomposition ...