Volume 8, issue 4 (2008)

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

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

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
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
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