Volume 8, issue 4 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Yang–Mills theory over surfaces and the Atiyah–Segal theorem

Daniel A Ramras

Algebraic & Geometric Topology 8 (2008) 2209–2251
Bibliography
1 R Abraham, Differential topology, Lecture notes of Smale (1964)
2 R Abraham, J Robbin, Transversal mappings and flows, W. A. Benjamin (1967) MR0240836
3 A Adem, Characters and $K$–theory of discrete groups, Invent. Math. 114 (1993) 489 MR1244911
4 A Alekseev, A Malkin, E Meinrenken, Lie group valued moment maps, J. Differential Geom. 48 (1998) 445 MR1638045
5 M F Atiyah, Characters and cohomology of finite groups, Inst. Hautes Études Sci. Publ. Math. (1961) 23 MR0148722
6 M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523 MR702806
7 M F Atiyah, G B Segal, Equivariant $K$–theory and completion, J. Differential Geometry 3 (1969) 1 MR0259946
8 G Baumslag, E Dyer, A Heller, The topology of discrete groups, J. Pure Appl. Algebra 16 (1980) 1 MR549702
9 G Carlsson, Derived representation theory and the algebraic $K$–theory of fields arXiv:0810.4826
10 G Carlsson, Derived completions in stable homotopy theory, J. Pure Appl. Algebra 212 (2008) 550 MR2365333
11 G D Daskalopoulos, The topology of the space of stable bundles on a compact Riemann surface, J. Differential Geom. 36 (1992) 699 MR1189501
12 G D Daskalopoulos, K K Uhlenbeck, An application of transversality to the topology of the moduli space of stable bundles, Topology 34 (1995) 203 MR1308496
13 S K Donaldson, P B Kronheimer, The geometry of four-manifolds, Oxford Math. Monogr., Oxford Science Publ., The Clarendon Press, Oxford University Press (1990) MR1079726
14 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Math. Surveys and Monogr. 47, Amer. Math. Soc. (1997) MR1417719
15 A D Elmendorf, M A Mandell, Rings, modules, and algebras in infinite loop space theory, Adv. Math. 205 (2006) 163 MR2254311
16 B Fine, P Kirk, E Klassen, A local analytic splitting of the holonomy map on flat connections, Math. Ann. 299 (1994) 171 MR1273082
17 P Griffiths, J Harris, Principles of algebraic geometry, Pure and Applied Math., Wiley-Interscience (1978) MR507725
18 K Gruher, String topology of classifying spaces, PhD thesis, Stanford University (2007)
19 G Harder, M S Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann. 212 (1975) 215 MR0364254
20 A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354
21 G Higman, A finitely generated infinite simple group, J. London Math. Soc. 26 (1951) 61 MR0038348
22 H Hironaka, Triangulations of algebraic sets, from: "Algebraic geometry (Humboldt State Univ., Arcata, Calif., 1974)", Proc. Sympos. Pure Math. 29, Amer. Math. Soc. (1975) 165 MR0374131
23 N K Ho, The real locus of an involution map on the moduli space of flat connections on a Riemann surface, Int. Math. Res. Not. (2004) 3263 MR2096257
24 N K Ho, C C M Liu, Connected components of the space of surface group representations, Int. Math. Res. Not. (2003) 2359 MR2003827
25 N K Ho, C C M Liu, On the connectedness of moduli spaces of flat connections over compact surfaces, Canad. J. Math. 56 (2004) 1228 MR2102631
26 N K Ho, C C M Liu, Connected components of spaces of surface group representations. II, Int. Math. Res. Not. (2005) 959 MR2146187
27 N K Ho, C C M Liu, Yang–Mills connections on nonorientable surfaces, Comm. Anal. Geom. 16 (2008) 617 MR2429971
28 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
29 J Kurzweil, On approximation in real Banach spaces, Studia Math. 14 (1955) 214 MR0068732
30 S Lang, Differential and Riemannian manifolds, Graduate Texts in Math. 160, Springer (1995) MR1335233
31 T Lawson, Derived representation theory of nilpotent groups, PhD thesis, Stanford University (2004)
32 T Lawson, The product formula in unitary deformation $K$–theory, $K$–Theory 37 (2006) 395 MR2269819
33 T Lawson, The Bott cofiber sequence in deformation $K$–theory and simultaneous similarity in $U(n)$, to appear in Math. Proc. Cambridge Philos. Soc. (2008)
34 W Lück, Rational computations of the topological $K$–theory of classifying spaces of discrete groups, J. Reine Angew. Math. 611 (2007) 163 MR2361088
35 W Lück, B Oliver, The completion theorem in $K$–theory for proper actions of a discrete group, Topology 40 (2001) 585 MR1838997
36 D McDuff, G Segal, Homology fibrations and the “group-completion” theorem, Invent. Math. 31 (1976) 279 MR0402733
37 J Milnor, Construction of universal bundles. II, Ann. of Math. $(2)$ 63 (1956) 430 MR0077932
38 P K Mitter, C M Viallet, On the bundle of connections and the gauge orbit manifold in Yang–Mills theory, Comm. Math. Phys. 79 (1981) 457 MR623962
39 S Morita, Geometry of characteristic classes, Transl. of Math. Monogr. 199, Amer. Math. Soc. (2001) MR1826571
40 S Morita, Geometry of differential forms, Trans. of Math. Monogr. 201, Amer. Math. Soc. (2001) MR1851352
41 D H Park, D Y Suh, Linear embeddings of semialgebraic $G$–spaces, Math. Z. 242 (2002) 725 MR1981195
42 J Råde, On the Yang–Mills heat equation in two and three dimensions, J. Reine Angew. Math. 431 (1992) 123 MR1179335
43 D Ramras, The Yang–Mills stratification for surfaces revisited arXiv:0805.2587
44 D A Ramras, Excision for deformation $K$–theory of free products, Algebr. Geom. Topol. 7 (2007) 2239 MR2366192
45 D Ramras, Stable representation theory of infinite discrete groups, PhD thesis, Stanford University (2007)
46 G Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. (1968) 105 MR0232393
47 G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
48 M R Sepanski, Compact Lie groups, Graduate Texts in Math. 235, Springer (2007) MR2279709
49 M Thaddeus, An introduction to the topology of the moduli space of stable bundles on a Riemann surface, from: "Geometry and physics (Aarhus, 1995)" (editors J E Andersen, J Dupont, H Pedersen, A Swann), Lecture Notes in Pure and Appl. Math. 184, Dekker (1997) 71 MR1423157
50 K K Uhlenbeck, Connections with $L^{p}$ bounds on curvature, Comm. Math. Phys. 83 (1982) 31 MR648356
51 K Wehrheim, Uhlenbeck compactness, EMS Series of Lectures in Math., Eur. Math. Soc. (2004) MR2030823
52 H Whitney, Elementary structure of real algebraic varieties, Ann. of Math. $(2)$ 66 (1957) 545 MR0095844
53 A Wilansky, Topology for analysis, Robert E. Krieger Publishing Co. (1983) MR744674