Algebraic & Geometric Topology Volume 16, issue 2 (2016)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Spin structures on loop spaces that characterize string manifolds

Konrad Waldorf

Algebraic & Geometric Topology 16 (2016) 675–709

DOI: 10.2140/agt.2016.16.675

Bibliography

1	O Alvarez, T P Killingback, M Mangano, P Windey, The Dirac–Ramond operator in string theory and loop space index theorems, Nuclear Phys. B Proc. Suppl. 1A (1987) 189 MR1005560
2	O Alvarez, T P Killingback, M Mangano, P Windey, String theory and loop space index theorems, Comm. Math. Phys. 111 (1987) 1 MR896755
3	M F Atiyah, Circular symmetry and stationary-phase approximation, from: "Colloquium in honor of Laurent Schwartz, Vol. 1", Astérisque 131 (1985) 43 MR816738
4	C Bär, C Becker, Differential characters, 2112, Springer (2014) MR3237728
5	J L Brylinski, D A McLaughlin, The geometry of degree-four characteristic classes and of line bundles on loop spaces, I, Duke Math. J. 75 (1994) 603 MR1291698
6	A L Carey, S Johnson, M K Murray, D Stevenson, B L Wang, Bundle gerbes for Chern–Simons and Wess–Zumino–Witten theories, Comm. Math. Phys. 259 (2005) 577 MR2174418
7	A L Carey, M K Murray, String structures and the path fibration of a group, Comm. Math. Phys. 141 (1991) 441 MR1134932
8	T P Killingback, World-sheet anomalies and loop geometry, Nuclear Phys. B 288 (1987) 578 MR892061
9	K Kuribayashi, T Yamaguchi, The vanishing problem of the string class with degree 3, J. Austral. Math. Soc. Ser. A 65 (1998) 129 MR1646609
10	D A McLaughlin, Orientation and string structures on loop space, Pacific J. Math. 155 (1992) 143 MR1174481
11	J Mickelsson, Kac–Moody groups, topology of the Dirac determinant bundle, and fermionization, Comm. Math. Phys. 110 (1987) 173 MR887993
12	M K Murray, Bundle gerbes, J. London Math. Soc. 54 (1996) 403
13	T Nikolaus, K Waldorf, Four equivalent versions of nonabelian gerbes, Pacific J. Math. 264 (2013) 355 MR3089401
14	T Nikolaus, K Waldorf, Lifting problems and transgression for non-abelian gerbes, Adv. Math. 242 (2013) 50 MR3055987
15	K Pilch, N P Warner, String structures and the index of the Dirac–Ramond operator on orbifolds, Comm. Math. Phys. 115 (1988) 191 MR931661
16	A Pressley, G Segal, Loop groups, Oxford Univ. Press (1986) MR900587
17	M Spera, T Wurzbacher, Twistor spaces and spinors over loop spaces, Math. Ann. 338 (2007) 801 MR2317752
18	D Stevenson, Bundle 2–gerbes, Proc. London Math. Soc. 88 (2004) 405
19	S Stolz, P Teichner, What is an elliptic object?, from: "Topology, geometry and quantum field theory" (editor U Tillmann), London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 247 MR2079378
20	S Stolz, P Teichner, The spinor bundle on loop spaces (2005)
21	K Waldorf, More morphisms between bundle gerbes, Theory Appl. Categ. 18 (2007) 240 MR2318389
22	K Waldorf, Multiplicative bundle gerbes with connection, Differential Geom. Appl. 28 (2010) 313 MR2610397
23	K Waldorf, A loop space formulation for geometric lifting problems, J. Aust. Math. Soc. 90 (2011) 129 MR2810948
24	K Waldorf, A construction of string 2–group models using a transgression-regression technique, from: "Analysis, geometry and quantum field theory" (editors C L Aldana, M Braverman, B Iochum, C Neira Jiménez), Contemp. Math. 584, Amer. Math. Soc. (2012) 99 MR3013040
25	K Waldorf, Transgression to loop spaces and its inverse, I : Diffeological bundles and fusion maps, Cah. Topol. Géom. Différ. Catég. 53 (2012) 162 MR2905777
26	K Waldorf, Transgression to loop spaces and its inverse, II: Gerbes and fusion bundles with connection, preprint (2013) arXiv:1004.0031
27	K Waldorf, Transgression to loop spaces and its inverse, III : Gerbes and thin fusion bundles, Adv. Math. 231 (2012) 3445 MR2980505
28	K Waldorf, String connections and Chern–Simons theory, Trans. Amer. Math. Soc. 365 (2013) 4393 MR3055700
29	E Witten, The index of the Dirac operator in loop space, from: "Elliptic curves and modular forms in algebraic topology" (editor P S Landweber), Lecture Notes in Math. 1326, Springer (1988) 161 MR970288