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

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

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
The homology of the Temperley–Lieb algebras

Rachael Boyd and Richard Hepworth

Geometry & Topology 28 (2024) 1437–1499
Bibliography
1 A Björner, M Wachs, On lexicographically shellable posets, Trans. Amer. Math. Soc. 277 (1983) 323 MR0690055
2 C Bowman, A Cox, A Hazi, Path isomorphisms between quiver Hecke and diagrammatic Bott–Samelson endomorphism algebras, Adv. Math. 429 (2023) 109185 MR4611117
3 R Boyd, Homological stability for Artin monoids, Proc. Lond. Math. Soc. 121 (2020) 537 MR4100117
4 R Boyd, R Hepworth, Combinatorics of injective words for Temperley–Lieb algebras, J. Combin. Theory Ser. A 181 (2021) 105446 MR4235244
5 R Boyd, R Hepworth, P Patzt, The homology of the Brauer algebras, Selecta Math. 27 (2021) 85 MR4304560
6 J Brundan, A Kleshchev, Blocks of cyclotomic Hecke algebras and Khovanov–Lauda algebras, Invent. Math. 178 (2009) 451 MR2551762
7 R M Charney, Homology stability for GLn of a Dedekind domain, Invent. Math. 56 (1980) 1 MR0557579
8 T Church, Homological stability for configuration spaces of manifolds, Invent. Math. 188 (2012) 465 MR2909770
9 J Désarménien, Une autre interprétation du nombre de dérangements, Sém. Lothar. Combin. 8 (1983) 11
10 E Deutsch, L Shapiro, A survey of the Fine numbers, Discrete Math. 241 (2001) 241 MR1861421
11 C K Fan, R M Green, Monomials and Temperley–Lieb algebras, J. Algebra 190 (1997) 498 MR1441960
12 F D Farmer, Cellular homology for posets, Math. Japon. 23 (1979) 607 MR0529895
13 S Galatius, A Kupers, O Randal-Williams, Cellular Ek–algebras, preprint (2018) arXiv:1805.07184
14 J J Graham, G I Lehrer, Cellular algebras, Invent. Math. 123 (1996) 1 MR1376244
15 T Halverson, M Mazzocco, A Ram, Commuting families in Hecke and Temperley–Lieb algebras, Nagoya Math. J. 195 (2009) 125 MR2552957
16 J L Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math. 121 (1985) 215 MR0786348
17 A Hatcher, N Wahl, Stabilization for mapping class groups of 3–manifolds, Duke Math. J. 155 (2010) 205 MR2736166
18 R Hepworth, Homological stability for families of Coxeter groups, Algebr. Geom. Topol. 16 (2016) 2779 MR3572348
19 R Hepworth, Homological stability for Iwahori–Hecke algebras, J. Topol. 15 (2022) 2174 MR4584588
20 V F R Jones, Index for subfactors, Invent. Math. 72 (1983) 1 MR0696688
21 V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103 MR0766964
22 W van der Kallen, Homology stability for linear groups, Invent. Math. 60 (1980) 269 MR0586429
23 C Kassel, V Turaev, Braid groups, 247, Springer (2008) MR2435235
24 L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR0899057
25 L H Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990) 417 MR0958895
26 L H Kauffman, Knot diagrammatics, from: "Handbook of knot theory" (editors W Menasco, M Thistlethwaite), Elsevier (2005) 233 MR2179264
27 L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of 3–manifolds, 134, Princeton Univ. Press (1994) MR1280463
28 M C Kerz, The complex of words and Nakaoka stability, Homology Homotopy Appl. 7 (2005) 77 MR2155519
29 W B R Lickorish, Calculations with the Temperley–Lieb algebra, Comment. Math. Helv. 67 (1992) 571 MR1185809
30 H Maazen, Homology stability for the general linear group, PhD thesis, Utrecht University (1979)
31 M Nakaoka, Decomposition theorem for homology groups of symmetric groups, Ann. of Math. 71 (1960) 16 MR0112134
32 D Quillen, On the cohomology and K–theory of the general linear groups over a finite field, Ann. of Math. 96 (1972) 552 MR0315016
33 O Randal-Williams, Homological stability for unordered configuration spaces, Q. J. Math. 64 (2013) 303 MR3032101
34 O Randal-Williams, Resolutions of moduli spaces and homological stability, J. Eur. Math. Soc. 18 (2016) 1 MR3438379
35 O Randal-Williams, A remark on the homology of Temperley–Lieb algebras, preprint (2021)
36 D Ridout, Y Saint-Aubin, Standard modules, induction and the structure of the Temperley–Lieb algebra, Adv. Theor. Math. Phys. 18 (2014) 957 MR3281274
37 N J A Sloane, Jacobsthal sequence (or Jacobsthal numbers) : a(n) = a(n 1) + 2 a(n 2), with a(0) = 0, a(1) = 1 ; also a(n) = nearest integer to 2n3, from: "The on-line encyclopedia of integer sequences" (2000)
38 R Spencer, Jacobsthal elements, web resource (2022)
39 R A Spencer, The modular Temperley–Lieb algebra, Rocky Mountain J. Math. 53 (2023) 177 MR4585987
40 R J Sroka, The homology of a Temperley–Lieb algebra on an odd number of strands, (2022) arXiv:2202.08799
41 M Szymik, N Wahl, The homology of the Higman–Thompson groups, Invent. Math. 216 (2019) 445 MR3953508
42 H N V Temperley, E H Lieb, Relations between the “percolation” and “colouring” problem and other graph-theoretical problems associated with regular planar lattices : some exact results for the “percolation” problem, Proc. Roy. Soc. Lond. Ser. A 322 (1971) 251 MR0498284
43 B Webster, The existence of Jones–Wenzl projectors, (2017) MR3624396
44 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
45 H Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9 (1987) 5 MR0873400
46 B W Westbury, The representation theory of the Temperley–Lieb algebras, Math. Z. 219 (1995) 539 MR1343661