Volume 18, issue 3 (2014)

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

Volume 29, 1 issue Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
A categorification of $\boldsymbol{U}_T(\mathfrak{sl}(1|1))$ and its tensor product representations

Yin Tian

Geometry & Topology 18 (2014) 1635–1717
Bibliography
1 G Benkart, D Moon, Planar rook algebras and tensor representations of gl(1|1), arXiv:1201.2482
2 J Bernstein, V Lunts, Equivariant sheaves and functors, 1578, Springer, Berlin (1994) MR1299527
3 S Bigelow, E Ramos, R Yi, The Alexander and Jones polynomials through representations of rook algebras, J. Knot Theory Ramifications 21 (2012) 1250114, 18 MR2978881
4 J Chuang, R Rouquier, Derived equivalences for symmetric groups and sl2–categorification, Ann. of Math. 167 (2008) 245 MR2373155
5 L Crane, I B Frenkel, Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, J. Math. Phys. 35 (1994) 5136 MR1295461
6 D Flath, T Halverson, K Herbig, The planar rook algebra and Pascal’s triangle, Enseign. Math. (2) 55 (2009) 77 MR2541502
7 E Giroux, Structures de contact sur les variétés fibrées en cercles audessus d’une surface, Comment. Math. Helv. 76 (2001) 218 MR1839346
8 K Honda, Contact structures, Heegaard–Floer homology and triangulated categories, in preparation
9 K Honda, On the classification of tight contact structures, I, Geom. Topol. 4 (2000) 309 MR1786111
10 K Honda, Gluing tight contact structures, Duke Math. J. 115 (2002) 435 MR1940409
11 K Honda, W H Kazez, G Matić, Pinwheels and bypasses, Algebr. Geom. Topol. 5 (2005) 769 MR2153107
12 K Honda, W H Kazez, G Matić, Right-veering diffeomorphisms of compact surfaces with boundary, II, Geom. Topol. 12 (2008) 2057 MR2431016
13 K Honda, W H Kazez, G Matić, The contact invariant in sutured Floer homology, Invent. Math. 176 (2009) 637 MR2501299
14 Y Huang, Bypass attachments and homotopy classes of 2–plane fields in contact topology, arXiv:1105.2348
15 L H Kauffman, H Saleur, Free fermions and the Alexander–Conway polynomial, Comm. Math. Phys. 141 (1991) 293 MR1133269
16 B Keller, On differential graded categories, from: "International Congress of Mathematicians, Vol. II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc., Zürich (2006) 151 MR2275593
17 M Khovanov, How to categorify one-half of quantum gl(1|2), arXiv:1007.3517
18 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
19 M Khovanov, A D Lauda, A categorification of quantum sl(n), MR2628852
20 M Khovanov, A D Lauda, A diagrammatic approach to categorification of quantum groups, I, Represent. Theory 13 (2009) 309 MR2525917
21 M Khovanov, A D Lauda, A diagrammatic approach to categorification of quantum groups, II, Trans. Amer. Math. Soc. 363 (2011) 2685 MR2763732
22 A D Lauda, A categorification of quantum sl(2), Adv. Math. 225 (2010) 3327 MR2729010
23 R Lipshitz, P Ozsváth, D Thurston, Bordered Heegaard–Floer homology : Invariance and pairing, arXiv:0810.0687
24 S Makar-Limanov, Morse surgeries of index 0 on tight manifolds, Preprint (1997)
25 C Manolescu, P Ozsváth, S Sarkar, A combinatorial description of knot Floer homology, Ann. of Math. 169 (2009) 633 MR2480614
26 D Mathews, Chord diagrams, contact-topological quantum field theory and contact categories, Algebr. Geom. Topol. 10 (2010) 2091 MR2745667
27 D V Mathews, Sutured TQFT, torsion and tori, Internat. J. Math. 24 (2013) 1350039, 35 MR3070808
28 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
29 P Ozsváth, Z Szabó, Heegaard–Floer homology and contact structures, Duke Math. J. 129 (2005) 39 MR2153455
30 J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003)
31 N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
32 R Rouquier, 2–Kac–Moody algebras, arXiv:0812.5023
33 L Rozansky, H Saleur, Quantum field theory for the multivariable Alexander–Conway polynomial, Nuclear Phys. B 376 (1992) 461 MR1170953
34 A Sartori, Categorification of tensor powers of the vector representation of Uq(gl(1|1)), arXiv:1305.6162
35 L Solomon, Representations of the rook monoid, J. Algebra 256 (2002) 309 MR1939108
36 Y Tian, Categorical braid group actions on representations of TEXTBACKSLASHmathboldTEXTBACKSLASHUT(sl(1|1)), in preparation
37 Y Tian, A categorification of TEXTBACKSLASHmathboldTEXTBACKSLASHUq(sl(1|1)) as an algebra arXiv:1210.5680
38 B Webster, Knot invariants and higher representation theory I : Diagrammatic and geometric categorification of tensor products, arXiv:1001.2020
39 B Webster, Knot invariants and higher representation theory II : The categorification of quantum knot invariants, arXiv:1005.4559
40 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
41 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772
42 R Zarev, Bordered Floer homology for sutured manifolds, arXiv:0908.1106
43 R Zarev, Equivalence of gluing maps for SFH, in preparation