Volume 14, issue 4 (2014)

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

Volume 20
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
One-dimensional Chern–Simons theory and the $\hat{A}$ genus

Owen Gwilliam and Ryan Grady

Algebraic & Geometric Topology 14 (2014) 2299–2377
1 M Alexandrov, A Schwarz, O Zaboronsky, M Kontsevich, The geometry of the master equation and topological quantum field theory, Internat. J. Modern Phys. A 12 (1997) 1405 MR1432574
2 M F Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957) 181 MR0086359
3 D Ben-Zvi, D Nadler, Loop spaces and connections, (2011) arXiv:1002.3636v2
4 N Berline, E Getzler, M Vergne, Heat kernels and Dirac operators, Grundl. Math. Wissen. 298, Springer (1992) MR1215720
5 I N Bernšteĭn, B I Rosenfel’d, Homogeneous spaces of infinite-dimensional Lie algebras and the characteristic classes of foliations, Uspehi Mat. Nauk 28 (1973) 103 MR0415633
6 R Bezrukavnikov, D Kaledin, Fedosov quantization in algebraic context, Mosc. Math. J. 4 (2004) 559, 782 MR2119140
7 P Bressler, R Nest, B Tsygan, Riemann–Roch theorems via deformation quantization, I, II, Adv. Math. 167 (2002) 1, 26 MR1901245
8 D Calaque, M Van den Bergh, Hochschild cohomology and Atiyah classes, Adv. Math. 224 (2010) 1839 MR2646112
9 D Calaque, C A Rossi, Lectures on Duflo isomorphisms in Lie algebra and complex geometry, Eur. Math. Soc. (2011) MR2816610
10 A Căldăraru, The Mukai pairing, II: The Hochschild–Kostant–Rosenberg isomorphism, Adv. Math. 194 (2005) 34 MR2141853
11 A Căldăraru, S Willerton, The Mukai pairing, I: A categorical approach, New York J. Math. 16 (2010) 61 MR2657369
12 A S Cattaneo, G Felder, L Tomassini, From local to global deformation quantization of Poisson manifolds, Duke Math. J. 115 (2002) 329 MR1944574
13 Z Chen, M Stiénon, P Xu, From Atiyah classes to homotopy Leibniz algebras, arXiv:1204.1075
14 K Costello, A geometric construction of the Witten genus, I, arXiv:1006.5422
15 K Costello, A geometric construction of the Witten genus, II, arXiv:1112.0816
16 K Costello, Renormalization and effective field theory, Mathematical Surveys and Monographs 170, Amer. Math. Soc. (2011) MR2778558
17 K Costello, O Gwilliam, Factorization algebras in quantum field theory, (2014)
18 P Deligne, P Etingof, D S Freed, L C Jeffrey, D A Každan, J W Morgan, D R Morrison, E Witten, editors, Quantum fields and strings: A course for mathematicians. Vol. 1, 2, Amer. Math. Soc. (1999) MR1701618
19 V Dolgushev, A formality theorem for Hochschild chains, Adv. Math. 200 (2006) 51 MR2199629
20 B V Fedosov, A simple geometrical construction of deformation quantization, J. Differential Geom. 40 (1994) 213 MR1293654
21 B V Fedosov, Deformation quantization and index theory, Mathematical Topics 9, Akademie Verlag (1996) 325 MR1376365
22 J Francis, The tangent complex and Hochschild cohomology of $\mathscr{E}_n$–rings, Compos. Math. 149 (2013) 430 MR3040746
23 E Frenkel, D Ben-Zvi, Vertex algebras and algebraic curves, Mathematical Surveys and Monographs 88, Amer. Math. Soc. (2004) MR2082709
24 I M Gel’fand, D A Každan, Some problems of differential geometry and the calculation of cohomologies of Lie algebras of vector fields, Sov. Math., Dokl. 12 (1971) 1367
25 I M Gel’fand, D A Každan, D B Fuks, Actions of infinite-dimensional Lie algebras, Funkcional. Anal. i Priložen. 6 (1972) 10 MR0301767
26 E Getzler, Pseudodifferential operators on supermanifolds and the Atiyah–Singer index theorem, Comm. Math. Phys. 92 (1983) 163 MR728863
27 P B Gilkey, Invariance theory, the heat equation, and the Atiyah–Singer index theorem, CRC Press (1995) MR1396308
28 R Grady, The $\hat{A}$–genus as a projective volume form on the derived loop space, arXiv:1211.6816
29 R Grady, On geometric aspects of topological quantum mechanics, PhD thesis, University of Notre Dame (2012)
30 R Grady, O Gwilliam, ${L}_{\infty}$ spaces and derived loop spaces, arXiv:1404.5426
31 F Hirzebruch, Topological methods in algebraic geometry, Classics in Mathematics, Springer (1995) MR1335917
32 F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, Aspects of Mathematics E20, Friedr. Vieweg & Sohn (1992) MR1189136
33 L Illusie, Complexe cotangent et déformations, I, Lecture Notes in Mathematics 239, Springer (1971) MR0491680
34 C Itzykson, J M Luck, P Moussa, M Waldschmidt, editors, From number theory to physics, Springer (1992) MR1221099
35 M Kapranov, Rozansky–Witten invariants via Atiyah classes, Compositio Math. 115 (1999) 71 MR1671737
36 N Markarian, The Atiyah class, Hochschild cohomology and the Riemann–Roch theorem, J. Lond. Math. Soc. 79 (2009) 129 MR2472137
37 M J Pflaum, H Posthuma, X Tang, Cyclic cocycles on deformation quantizations and higher index theorems, Adv. Math. 223 (2010) 1958 MR2601006
38 A C Ramadoss, The big Chern classes and the Chern character, Internat. J. Math. 19 (2008) 699 MR2431634
39 M Schlessinger, J Stasheff, The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra 38 (1985) 313 MR814187
40 B Toën, G Vezzosi, Chern character, loop spaces and derived algebraic geometry, from: "Algebraic topology" (editors N A Baas, E M Friedlander, B Jahren, P A Østvær), Abel Symp. 4, Springer (2009) 331 MR2597742
41 B Tsygan, Formality conjectures for chains, from: "Differential topology, infinite-dimensional Lie algebras, and applications" (editors A Astashkevich, S Tabachnikov), Amer. Math. Soc. Transl. Ser. 2 194, Amer. Math. Soc. (1999) 261 MR1729368
42 T Willwacher, Formality of cyclic chains, Int. Math. Res. Not. 2011 (2011) 3939 MR2836399
43 P Windey, Supersymmetric quantum mechanics and the Atiyah–Singer index theorem, Acta Phys. Polon. B 15 (1984) 435 MR757583
44 E Witten, Constraints on supersymmetry breaking, Nuclear Phys. B 202 (1982) 253 MR668987