Volume 8, issue 3 (2008)

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Nontrivalent graph cocycle and cohomology of the long knot space

Keiichi Sakai

Algebraic & Geometric Topology 8 (2008) 1499–1522
Bibliography
1 S Axelrod, I M Singer, Chern–Simons perturbation theory. II, J. Differential Geom. 39 (1994) 173 MR1258919
2 R Bott, C Taubes, On the self-linking of knots, J. Math. Phys. 35 (1994) 5247 MR1295465
3 R Budney, Little cubes and long knots, Topology 46 (2007) 1 MR2288724
4 R Budney, F Cohen, On the homology of the space of knots arXiv:math.GT/0504206
5 A S Cattaneo, P Cotta-Ramusino, R Longoni, Configuration spaces and Vassiliev classes in any dimension, Algebr. Geom. Topol. 2 (2002) 949 MR1936977
6 F R Cohen, The homology of $\mathcal{C}_{n+1}$–space, $n{\geq}0$, Lecture Notes in Math. 533, Springer (1976) MR0436146
7 T Kohno, Vassiliev invariants and de Rham complex on the space of knots, from: "Symplectic geometry and quantization (Sanda and Yokohama, 1993)", Contemp. Math. 179, Amer. Math. Soc. (1994) 123 MR1319605
8 P Lambrechts, V Tourtchine, I Volić, The rational homology of spaces of knots in codimension $\gt 2$ arXiv:math.AT/0703649
9 R Longoni, Nontrivial classes in $H^*(\mathrm{Imb}(S^1,\mathbb{R}^n))$ from nontrivalent graph cocycles, Int. J. Geom. Methods Mod. Phys. 1 (2004) 639 MR2095442
10 J P May, The geometry of iterated loop spaces, Lecture Notes in Math. 271, Springer (1972) MR0420610
11 J E McClure, J H Smith, Cosimplicial objects and little $n$–cubes. I, Amer. J. Math. 126 (2004) 1109 MR2089084
12 K Sakai, Poisson structures on the homology of the space of knots, from: "Groups, homotopy and configuration spaces (Tokyo 2005)" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13 (2008) 463
13 P Salvatore, Knots, operads, and double loop spaces, Int. Math. Res. Not. (2006) 22 MR2276349
14 D P Sinha, The topology of spaces of knots arXiv:math.AT/0202287
15 D P Sinha, Manifold-theoretic compactifications of configuration spaces, Selecta Math. $($N.S.$)$ 10 (2004) 391 MR2099074
16 D P Sinha, Operads and knot spaces, J. Amer. Math. Soc. 19 (2006) 461 MR2188133
17 V Tourtchine, On the other side of the bialgebra of chord diagrams, J. Knot Theory Ramifications 16 (2007) 575 MR2333307
18 I Volić, A survey of Bott–Taubes integration, J. Knot Theory Ramifications 16 (2007) 1 MR2300426