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The School of Mathematics carries out research in a wide variety of areas of the mathematical sciences, including pure, applied, statistics, operational research as well as mathematical physics.

### Recent Submissions

• #### Representations of algebras as universal localizations ﻿

(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 ...
• #### Frobenius n-homomorphisms, transfers and branched coverings ﻿

(2008-01-01)
The main purpose is to characterise continuous maps that are n-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius nhomomorphisms between two function spaces that ...
• #### Averages in vector spaces over finite fields ﻿

(2008-01-01)
We study the analogues of the problems of averages and maximal averages over a surface in R-n when the euclidean structure is replaced by that of a vector space over a finite field, and obtain optimal results in a number ...
• #### On the lines passing through two conjugates of a Salem number ﻿

(2008-01-01)
We show that the number of distinct non-parallel lines passing through two conjugates of an algebraic number alpha of degree d >= 3 is at most [d(2)/2] - d + 2, its conjugates being in general position if this number is ...
• #### Blanchfield and Seifert algebra in high-dimensional boundary link theory I. Algebraic K-theory ﻿

(2006-11-01)
The classification of high-dimensional μ–component boundary links motivates decomposition theorems for the algebraic K–groups of the group ring A[Fμ] and the noncommutative Cohn localization Σ-1A[Fμ], for any μ≥1 and an ...
• #### Homology Manifold Bordism ﻿

(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 ﻿

(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 ...
• #### 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 ...
• #### A SURVEY OF WALL'S FINITENESS OBSTRUCTION ﻿

(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 ...
• #### An introduction to algebraic surgery ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### 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 ...
• #### 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.
• #### 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 ...
• #### NONCOMMUTATIVE LOCALIZATION AND CHAIN COMPLEXES I. ALGEBRAIC K- AND L-THEORY ﻿

(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 ﻿

(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 ...
• #### 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.
• #### 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 ...
• #### 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 ...