Now showing items 1-20 of 24

  • Homology Manifold Bordism 

    Johnston, Heather; Ranicki, Andrew (American Mathematical Society, 1999)
    The Bryant-Ferry-Mio-Weinberger surgery exact sequence for high-dimensional compact ANR homology manifolds is used to obtain transversality, splitting and bordism results for homology manifolds, generalizing previous work ...
  • C. T. C. Wall's contributions to the topology of manifolds 

    Ranicki, Andrew; Cappell, Sylvain; Rosenberg, Jonathan (Princeton, 2000)
    C. T. C. Wall spent the first half of his career, roughly from 1959 to 1977, working in topology and related areas of algebra. In this period, he produced more than 90 research papers and two books. Above all, Wall was ...
  • A SURVEY OF WALL'S FINITENESS OBSTRUCTION 

    Ferry, Steve; Ranicki, Andrew (http://arxiv.org/abs/math.AT/0008070,, 2000)
    Wall's finiteness obstruction is an algebraic K-theory invariant which decides if a finitely dominated space is homotopy equivalent to a finite CW complex. The invariant was originally formulated in the context of surgery ...
  • THE WHITEHEAD GROUP OF THE NOVIKOV RING 

    Ranicki, Andrew; Pajitnov, Andrei (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 ...
  • An introduction to algebraic surgery 

    Ranicki, Andrew (http://arxiv.org/pdf/math.AT/0008071, 2000)
    Surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory, without ...
  • ALGEBRAIC POINCARE COBORDISM 

    Ranicki, Andrew (http://arxiv.org/abs/math.AT/0008228,, 2001)
    The object of this paper is to give a reasonably leisurely account of the algebraic Poincare cobordism theory of Ranicki and the further development due to Weiss , along with some of the applications to manifolds and ...
  • THE ALGEBRAIC CONSTRUCTION OF THE NOVIKOV COMPLEX OF A CIRCLE-VALUED MORSE FUNCTION 

    Ranicki, Andrew (Springer-Verlag, 2001-06-29)
    The Novikov complex of a circle-valued Morse function f : M ! S is constructed algebraically from the Morse-Smale complex of the restriction of the real-valued Morse function f : M ! R to a fundamental domain of the ...
  • NONCOMMUTATIVE LOCALIZATION AND CHAIN COMPLEXES I. ALGEBRAIC K- AND L-THEORY 

    Neeman, Amnon; Ranicki, Andrew (2001-09-18)
    The noncommutative (Cohn) localization (sigma)^−1 R of a ring R is defined for any collection (sigma) of morphisms of f.g. projective left R-modules. We exhibit (sigma)^−1 R as the endomorphism ring of R in an appropriate ...
  • CONTROLLED SURGERY WITH TRIVIAL LOCAL FUNDAMENTAL GROUPS 

    Pedersen, Erik; Quinn, Frank; Ranicki, Andrew (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 ...
  • The structure set of an arbitrary space, the algebraic surgery exact sequence and the total surgery obstruction 

    Ranicki, Andrew (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 ...
  • Circle valued Morse theory and Novikov homology 

    Ranicki, Andrew (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 

    Ranicki, Andrew (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.
  • REPRESENTATIONS OF ALGEBRAS AS UNIVERSAL LOCALIZATIONS 

    Neeman, Amnon; Ranicki, Andrew; Schofield, Aiden (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 ...
  • Blanchfield and Seifert algebra in high dimensional knot theory 

    Ranicki, Andrew (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 ...
  • ON THE CALCULATION OF UNIL 

    Ranicki, Andrew; Connolly, Frank (2003-04-02)
    Cappell’s codimension 1 splitting obstruction surgery group UNiln is a direct summand of the Wall surgery obstruction group of an amalgamated free product. For any ring with involution R we use the quadratic Poincar´e ...
  • Generalized Arf invariants in algebraic L-theory 

    Ranicki, Andrew; Banagl, Markus (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 ...
  • Rigidity and gluing for Morse and Novikov complexes 

    Ranicki, Andrew; Cornea, Octav (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 ...
  • ALGEBRAIC AND COMBINATORIAL CODIMENSION 1 TRANSVERSALITY 

    Ranicki, Andrew (Submitted to the Proceedings of the Cassonfest (Austin, Texas, May 2003), 2003-08-12)
    The Waldhausen construction of Mayer-Vietoris splittings for chain complexes over an injective generalized free product is extended to Seifert-van Kampen splittings for CW complexes with fundamental group an injective ...
  • Noncommutative localization in topology 

    Ranicki, Andrew (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 ...
  • Representations of algebras as universal localizations 

    Ranicki, Andrew; Schofield, A.; Neeman, A. (2004-01-01)
    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 ...