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From August 1, 2004 I will be at the department of mathematics at the University of Bergen. The addresses below will be functional throughout the fall 2004, but snailmailing should be restricted to Bergen, cf. details on my Bergenske home page.
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Some interests
(Algebraic) K-theory, (motivic) homotopy theory, (topological)
cyclic homology and so on
Some links:
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My bookmarks (not regularly updated), https:innsida.ntnu.no/
- Mathematics Information servers (Penn State), List of useful preprint servers and electronic journals , The XY-Pic manual
- Karen og Vår's Home page, RERNG, A Curriculum Vitae. A fan club. A web and teaching report.
- Mathematics Information servers (Penn State), List of useful preprint servers and electronic journals , The XY-Pic manual
Papers
- Dundas, Bjørn Ian. Fibrations and homology sphere bordism.
Math. Scand. 72 (1993), no. 1, 20--28. 57Q20 (55R05)
- Dundas, Bjørn Ian; McCarthy, Randy. Stable $K$-theory and topological Hochschild homology. Ann. of Math. (2) 140 (1994), no. 3, 685--701. 19D55 (18G60 19D06)
- Dundas, Bjørn Ian; McCarthy, Randy. Topological Hochschild homology of ring functors and exact categories. J. Pure Appl. Algebra 109 (1996), no. 3, 231--294. 19D55 (16E40 18G30 18G60)
- Dundas, Bjørn Ian. Relative K-theory and topological cyclic homology. Acta Math. 179 (1997), no. 2, 223--242. 19D55
- Dundas, Bjørn Ian. K-theory theorems in topological cyclic homology. J. Pure Appl. Algebra 129 (1998), no. 1, 23--33. 19-XX (16Exx)
- Dundas, Bjørn Ian. Continuity of K-theory: an example in equal characteristics. Proc. Amer. Math. Soc. 126 (1998), no. 5, 1287--1291. 11Sxx (13Jxx 19D45 19D55)
- Dundas, Bjørn Ian. Degreewise K-theory. K-theory 18 (1999), 77--92. 19D06, 18G30, 19D25, 16N20
- Dundas, Bjørn Ian. The Cyclotomic trace for symmetric monoidal categories. in "Geometry and Topology: Aarhus, Contemp. Math. 258 (2000), p. 121--144.
- Dundas, Bjørn Ian. Localization of V-categories. Theory Appl. Cat. 8 (2001), pp. 284-312
- Dundas, Bjørn Ian; Röndigs, Oliver and Østvær, Paul Arne, Enriched functors and stable homotopy theory. Documenta Mathematica, Vol. 8 (2003), 409-488
- Dundas, Bjørn Ian; Röndigs, Oliver and Østvær, Paul Arne, Motivic Functors, Documenta Mathematica, Vol. 8 (2003), 489-525
- Baas, Nils A.; Dundas, Bjørn Ian and Rognes, John Two-vector bundles and forms of elliptic cohomology. In Topology, Geometry and Quantum Field Theory, LMS Lecture note series 308, Cambridge University Press. Ed. Ulrike Tillmann (2004), p. 18--45.
- Dundas, Bjørn Ian; McCarthy, Randy. Stable $K$-theory and topological Hochschild homology. Ann. of Math. (2) 140 (1994), no. 3, 685--701. 19D55 (18G60 19D06)
Some unpublished papers
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The cyclotomic trace for S-algebras. To appear in
the Journal of the
London Mathematical Society.
Gives a functorial definition of the cyclotomic trace suitable
even when
the objects are not fibrant. As an application we give a
functorial and very
compact definition of the category of finitely generated free
A-modules for A an S-algebra which
pushes through the general machinery nicely.
- A model for the K-theory of complete extensions. An old unpublished note (Mar. 10. 1995). Some of the material is used in "The Local structure of algebraic K-theory", and will eventually appear there.
- The homology of additive categories. (April 25. 2001) Explains the connection between topological Hochschild homology and the homology of additive categories in the natural generality.
- A model for the K-theory of complete extensions. An old unpublished note (Mar. 10. 1995). Some of the material is used in "The Local structure of algebraic K-theory", and will eventually appear there.
Book projects
Differential Topology
(ps, pdf, US letter size). An introduction used for our course on manifolds at NTNU the last three years.
If you plan to use these notes as course material or otherwise have them tested on a wider audience, or if you just have some comments on the notes (apart from the fact that the file is upside-down: there was a bug in the computer program, and I did not care: just switch to sea-scape), please contact me.Gummistrikk-geometri - fra matematikkens skattekiste
joint with Nils Kristian Rossing. Vitensenteret i Trondheim, juli 2003, ISBN 82-92088-19-9. A popular exposition of some topological features (in Norwegian) written for teachers and other interested laymen. Available upon request, or buy it from Vitensenteret by sending a mail to postkasse at viten.ntnu.no.The Local structure of algebraic K-theory
joint with Tom G. Goodwillie and Randy McCarthy. Currently I am rewriting the thing so that it possibly can be readable. Here is the (ps,pdf)-file as it appeared on my screen June 9, 2004. Hopefully this epos is closing in on its final stage. There still is some cleaning up to do before it is presentable, but it certainly is getting more complete and is easier to maneuvre in now than last time it stalled in 2000 (which by most standards is a rather humble claim). Thanks to a number of people for helpful comments, in particular Morten Brun, Harald Kittang, John Rognes, Stefan Schwede, Paul Arne Østvær. Comments and corrections are very welcome!
