Papers

  • All my papers on the Arxiv (but exclude the Atiyah lectures!)
  • Codimension 2 embeddings, algebraic surgery and Seifert forms (with Maciej Borodzik and Andras Nemethi), e-print arxiv:1211.5964 (2012). Under revision
  • Solid angles and Seifert hypersurfaces (with Maciej Borodzik and Supreedee Dangskul) e-print arxiv:1706.06405 Submitted for publication (2017)
  • Signatures in algebra, topology and dynamics (with Etienne Ghys). Arxiv 1512.092582. Ensaios matematicos, Volume 30, 1-173 (2016)
    Mathematical Reviews, Zentralblatt review.
  • Morse theory for manifolds with boundary (with Maciej Borodzik and Andras Nemethi), e-print arxiv:1207.3066 (2012). Algebraic and Geometric Topology 16, 971-1023 (2016)
  • Commentary on the Kervaire-Milnor correspondence 1958-1961 (with Claude Weber), Bull. Amer. Math. Soc. 52, 603-609 (2015). Included in the October 2015 issue of the Bulletin of the American Mathematical Society devoted to the topologist John Milnor.
  • On the semicontinuity of the mod 2 spectrum of hypersurface singularities (with Maciej Borodzik and Andras Nemethi), e-print arxiv:1207.0798, Published in Journal of Algebraic Geometry 24, 379-398 (2015).
  • On the algebraic L-theory of Δ-sets (with Michael Weiss) e-print math.0701833.
    Pure and Applied Mathematics Quarterly (issue dedicated to F. Thomas Farrell and Lowell E. Jones) Vol. 8, 423--449 (2012)
  • Commentary on On the parallelizability of the spheres by R. Bott and J. Milnor and On the nonexistence of elements of Hopf invariant one by J. F. Adams, Bull. Amer. Math. Soc. 48, 509-511 (2011)
  • Algebraic K-theory over the infinite dihedral group: an algebraic approach, (with Jim Davis and Qayum Khan) e-print math.0803.1639
    Algebraic and Geometric Topology 11, 2391--2436 (2011)
  • The geometric Hopf invariant and double points (with Michael Crabb). e-print math.1002.2907
    J. of Fixed Point Theory and Applications 7, The Steve Smale Festschrift, 325--350 (2010)
  • Book review: The Novikov conjecture, geometry and algebra, by M.Kreck and W.Lück, Bull. L.M.S. 42, 181--183 (2010)
  • On the construction and topological invariance of the Pontryagin classes (with Michael Weiss). e-print math.0901.0819
    Geometriae Dedicata (issue dedicated to Bruce Williams) 148, 309--343 (2010)
  • A composition formula for manifold structures e-print math.0608705.
    Pure and Applied Mathematics Quarterly, Vol. 5 (2) (Hirzebruch 80th birthday issue), 701--727 (2009)
  • The signature of a fibre bundle is multiplicative mod 4 (with Ian Hambleton and Andrew Korzeniewski)
    Geometry & Topology 11, 251-314 (2007) e-print AT.0502353.
    Companion paper to Absolute Whitehead torsion (by Andrew Korzeniewski) Geometry & Topology 11, 215-249 (2007) e-print AT.0502349.
  • Blanchfield and Seifert algebra in high-dimensional boundary link theory I. Algebraic K-theory (with Des Sheiham)
    Geometry and Topology 10, 1761--1853 (2006) e-print AT.0508405.
  • The quadratic form E_8 and exotic homology manifolds (with Washington Mio), e-print AT.0403261
    Proceedings 2003 Oberwolfach meeting on exotic homology manifolds , Geometry and Topology Monograph 9, 33--66 (2006).
  • Controlled L-theory (with Masayuki Yamasaki) e-print AT.0402217
    in Proceedings 2003 Oberwolfach meeting on exotic homology manifolds , Geometry and Topology Monograph 9, 105--153 (2006)
  • Algebraic and combinatorial codimension 1 transversality e-print AT.0308111
    Geometry and Topology Monographs, Vol. 7 (2004), Proceedings of the Casson Fest, Paper no. 6, pages 145--180.
  • Generalized Arf invariants in algebraic L-theory (with Markus Banagl) e-print AT.0304362 Advances in Mathematics 199, 542-668 (2006)
  • On the calculation of UNil (with Frank Connolly) e-print AT.0304016, Advances in Mathematics 195, 205--258 (2005).
  • Noncommutative localization in topology e-print AT.0303046
    Proc. 2002 ICMS Edinburgh meeting on Noncommutative Localization in Algebra and Topology, LMS Lecture Notes Series 330 Cambridge University Press, 81--102 (2006).
  • Blanchfield and Seifert algebra in high-dimensional knot theory e-print GT.0212187
    Moscow Mathematical Journal 3, 1333-1367 (2003).
  • Rigidity and glueing for Morse and Novikov complexes (with Octav Cornea) e-print AT.0107221
    Journal of the European Mathematical Society 5, 343--394 (2003)
  • Representations of algebras as universal localizations (with Amnon Neeman and Aidan Schofield) e-print AT.0205034
    Mathematical Proceedings of the Cambridge Philosophical Society 136, 105--117 (2003)
  • Noncommutative localization in chain complexes I. Algebraic K- and L-theory. e-print RA.0109118 (2001) (with Amnon Neeman).
    The work in this e-print was subsequently divided into 3 papers:
    Noncommutative localisation in algebraic K-theory. I. Geometry and Topology 8 (2004), 1385--1425 (with Amnon Neeman).
    Noncommutative localisation in algebraic K-theory. II. Advances in Mathematics 213 (2007) 785--819 (by Amnon Neeman).
    Noncommutative localization in algebraic L-theory. Advances in Mathematics 220 (2009) 894--912.
  • Circle valued Morse theory and Novikov homology
    School on High-dimensional Manifold Topology, 543--569, ICTP Trieste (2002). e-print AT.0111317
  • The structure set of an arbitrary space, the algebraic surgery exact sequence and the total surgery obstruction
    School on High-dimensional Manifold Topology, 519--538, ICTP Trieste (2002). e-print AT.0111316
  • Foundations of algebraic surgery
    School on High-dimensional Manifold Topology, 495--514, ICTP Trieste (2002). e-print AT.0111315
  • Controlled surgery with trivial local fundamental groups (with Erik Pedersen and Frank Quinn) e-print AT.0111269
    Proceedings 2001 ICTP School on High-dimensional Manifold Topology, World Scientific, 421--426 (2003)
  • The algebraic construction of the Novikov complex of a circle-valued Morse function
    Mathematische Annalen 322, 745--785 (2002). The e-print AT.9903090 version has diagrams!
  • Algebraic Poincare cobordism
    in "Topology, geometry and algebra: interactions and new directions", Proc. 1999 Milgram Conference, Stanford,
    Contemporary Mathematics 279, A.M.S., 213--255 (2001), e-print AT.0008228
  • An introduction to algebraic surgery
    in Surveys on Surgery Theory, Vol. 2, Annals of Mathematics Studies 149, 81--163, Princeton (2001), e-print AT.0008071
  • A survey of Wall's finiteness obstruction (with Steve Ferry)
    in Surveys on Surgery Theory, Vol. 2, Annals of Mathematics Studies 149, 63--80, Princeton (2001), e-print AT.0008070
  • The Whitehead group of the Novikov ring (with Andrei Pajitnov) K-theory 21, 325--365 (2000) e-print AT.0012031
  • C.T.C. Wall's contributions to the topology of manifolds (with Sylvain Cappell and Jonathan Rosenberg)
    + Wall's publication list up to 1999, Surveys on Surgery Theory, Vol. 1, Annals of Mathematics Studies 145, 3--15, 17--24 , Princeton (2000)
  • Homology manifold bordism (with Heather Johnston) Trans. A.M.S. 352, 5093--5137 (2000), e-print AT.9909130
  • The Morse-Novikov theory of circle-valued functions and noncommutative localization (with Michael Farber)
    Proc. 1998 Moscow Conference for S.P.Novikov's 60th Birthday, Proc. Steklov Inst. 225, 381--388 (1999), e-print DG.9812122
  • Singularities, double points, controlled topology and chain duality
    Documenta Mathematica
    4, 1--59 (1999)
    Applications of chain duality to local invariants of Poincar\'e complexes and maps of manifolds, with homological obstructions answering:
    (1) Is a polyhedron with Poincar\'e duality a homology manifold?
    (2) Does a degree 1 PL map of polyhedral homology manifolds have acyclic point inverses?
    The paper may be regarded as a combinatorial introduction to controlled topology and surgery theory.
  • The Maslov index and the Wall signature non-additivity invariant Unpublished notes (1997)
  • Notes on Reidemeister torsion Unpublished notes (1997)
  • Controlled L-theory (Preliminary announcement) (with Masayuki Yamasaki)
    The extension to L-theory of Controlled K-theory. Proceedings of Sakado Conference on Surgery and Geometric Topology
    Science Bulletin of Josai University 2, 119--136 (1997)
  • On the Hauptvermutung
    Introductory survey published in the Hauptvermutung Book K-theory Monograph 1, Kluwer (1996)
  • Book review: The topological classification of stratified spaces, by S.Weinberger, Mathematical Review MR1308714 (96b:57024) (1996)
  • Bordism of automorphisms of manifolds from the algebraic L-theory point of view
    Proc. 1994 Princeton conference in honour of W.Browder,
    Ann. of Maths. Study 138, 314--327, Princeton University Press (1995)
  • On the Novikov conjecture
    Survey published in Novikov conjectures, Index theorems and Rigidity
    LMS Lecture Notes 226, 272--337, Cambridge University Press (1995)
  • A History and Survey of the Novikov Conjecture (with S.Ferry and J.Rosenberg)
    Published in Novikov conjectures, Index theorems and Rigidity
    LMS Lecture Notes 226, 7--66, Cambridge University Press (1995)
  • Controlled K-theory (with Masayuki Yamasaki)
    A self-contained account of the controlled algebraic K_0- and K_1-groups, including the applications to proofs of Chapman's result on the topological invariance of Whitehead torsion, and West's result on the homotopy finiteness of compact ANR's.
    Topology and Its Applications 61, 1--59 (1995)
  • Finite domination and Novikov rings
    The main result is that an infinite cyclic cover of a finite CW complex is finitely dominated if and only if the homology groups with coefficients in the Novikov rings are acyclic.
    Topology 34, 619--632 (1995)
    A message from Dan Grayson
    Zentralblatt review by Hans Munkholm
  • Symmetric and quadratic complexes with geometric control (with Masayuki Yamasaki)
    Proc. of Topology and Geometry Research Center, Kyungpook National University, Vol. 3, 139--152 (1993)
  • Surgery obstructions of fibre bundles (with Wolfgang Lueck)
    The generalization to surgery obstructions of the formulae of Atiyah, Lusztig and Meyer for the non-multiplicativity of the signature in a fibre bundle.
    Journal of Pure and Applied Algebra 81, 139--189 (1992)
  • The Maslov index and the Wall signature non-additivity invariant Unpublished paper (1991)
  • The L-theory of Laurent extensions and genus 0 function fields (with Jim Milgram)
    J. f. reine und angew. Math. 406, 121--166 (1990)
  • Chain complexes and assembly (with Michael Weiss)
    Math. Z. 204, 157--185 (1990)
  • Additive L-theory
    K-theory 3, 163--195 (1989)
  • Chain homotopy projections (with Wolfgang Lueck)
    J. Algebra 120, 361--391 (1989)
  • Jordan normal form projections (with K.Y.Lam and L.Smith)
    Archiv der Mathematik 50, 113--117 (1988)
  • Surgery transfer (with Wolfgang Lueck)
    Proceedings of 1987 Goettingen Topology conference
    Springer Lecture Notes 1361, 167--246 (1988)
  • Round L-theory (with Ian Hambleton and Larry Taylor)
    J. Pure and Applied Algebra 47, 131--154 (1987)
  • The L-theory of twisted quadratic extensions
    Can. J. Math. 39, 345--364 (1987)
  • Intrinsic transversality structures (with Norman Levitt)
    Pacific J. Math. 129, 85--144 (1987)
  • The algebraic theory of torsion II. Products
    K-theory 1, 115--170 (1987)
  • Semi-invariants in surgery (with Jim Davis)
    K-theory 1, 83--109 (1987)
  • Algebraic and geometric splittings of the K- and L-groups of polynomial extensions
    Proc. 1985 Poznan Topology Conf., Springer Lecture Notes 1217, 321--363 (1986)
  • The algebraic theory of torsion I.
    Proceedings of 1983 Rutgers Topology conference
    Springer Lecture Notes 1126, 199--237 (1985)
  • Some product formulae for nonsimply connected surgery problems (with Jim Milgram)
    Trans. A.M.S. 297, 383--413 (1985)
  • The algebraic theory of finiteness obstruction
    Math. Scand. 57, 105--126 (1985)
  • Book review: K-theory of forms, by A.Bak, Bull. A.M.S. 7, 279--280 (1982)
  • The projective class group transfer induced by an S1-bundle (with Hans Munkholm)
    Proc. 1981 London, Ontario Topology Conf., CMS Conf. Proc. 2, 461--484 (1982)
  • Projective surgery theory (with Erik Pedersen)
    Topology 19, 239--254 (1980)
  • The algebraic theory of surgery I.
    Proc. London Math. Soc. (3) 40, 87--192 (1980)
  • The algebraic theory of surgery II.
    Proc. London Math. Soc. (3) 40, 193--283 (1980)
  • The total surgery obstruction
    Proceedings of 1978 Arhus Topology conference
    Springer Lecture Notes 763, 275--316 (1979)
  • Localization in quadratic L-theory
    Proceedings of 1978 Waterloo Topology conference
    Springer Lecture Notes 741, 102--157 (1979)
  • The surgery obstruction of a disjoint union
    J. London Math. Soc. (2) 20, 559--566 (1979)
  • The algebraic theory of surgery (unpublished notes, Princeton, 1978)
    An algebraic formulation of surgery (unpublished research fellowship dissertation, Trinity College, Cambridge, 1972)
    Most of the material in the dissertation and notes was subsequently published in The algebraic theory of surgery I. and II.,
    Exact sequences in the algebraic theory of surgery, The total surgery obstruction and Algebraic L-theory and topological manifolds.
  • On the algebraic L-theory of semisimple rings
    J. Algebra 50, 242--243 (1978)
  • A semi-local combinatorial formula for the signature of a 4k-manifold (with Dennis Sullivan)
    J. Differential Geometry 11, 23--29 (1976)
  • Algebraic L-theory, IV: Polynomial extensions
    Comm. Math. Helv. 49, 137--167 (1974)
  • Algebraic L-theory, III: Twisted Laurent extensions
    Proc. 1972 Battelle Seattle Algebraic K-theory Conf., Vol. III., Springer Lecture Notes 343, 412--463 (1973)
  • Algebraic L-theory, II: Laurent extensions
    Proc. London Math. Soc. (3) 27, 126--158 (1973)
  • Algebraic L-theory, I: Foundations
    Proc. London Math. Soc. (3) 27, 101--125 (1973)