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

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Topological finiteness properties of monoids, I: Foundations

Robert D Gray and Benjamin Steinberg

Algebraic & Geometric Topology 22 (2022) 3083–3170
Bibliography
1 W W Adams, M A Rieffel, Adjoint functors and derived functors with an application to the cohomology of semigroups, J. Algebra 7 (1967) 25 MR218423
2 J M Alonso, S M Hermiller, Homological finite derivation type, Internat. J. Algebra Comput. 13 (2003) 341 MR2000876
3 D J Anick, On the homology of associative algebras, Trans. Amer. Math. Soc. 296 (1986) 641 MR846601
4 M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
5 R Bieri, Homological dimension of discrete groups, Queen Mary College (1976) MR0466344
6 R Bieri, J Harlander, On the FP3–conjecture for metabelian groups, J. London Math. Soc. 64 (2001) 595 MR1865552
7 R Bieri, B Renz, Valuations on free resolutions and higher geometric invariants of groups, Comment. Math. Helv. 63 (1988) 464 MR960770
8 R V Book, F Otto, String-rewriting systems, Springer (1993) MR1215932
9 K S Brown, Finiteness properties of groups, J. Pure Appl. Algebra 44 (1987) 45 MR885095
10 K S Brown, The geometry of rewriting systems : a proof of the Anick–Groves–Squier theorem, from: "Algorithms and classification in combinatorial group theory" (editors G Baumslag, C F I Miller), Math. Sci. Res. Inst. Publ. 23, Springer (1992) 137 MR1230632
11 K S Brown, Cohomology of groups, 87, Springer (1994) MR1324339
12 K S Brown, Lectures on the cohomology of groups, from: "Cohomology of groups and algebraic K–theory" (editors L Ji, K Liu, S T Yau), Adv. Lect. Math. 12, International (2010) 131 MR2655176
13 K S Brown, R Geoghegan, An infinite-dimensional torsion-free FP group, Invent. Math. 77 (1984) 367 MR752825
14 K U Bux, K Wortman, Finiteness properties of arithmetic groups over function fields, Invent. Math. 167 (2007) 355 MR2270455
15 J Cassaigne, P V Silva, Infinite periodic points of endomorphisms over special confluent rewriting systems, Ann. Inst. Fourier (Grenoble) 59 (2009) 769 MR2521435
16 M K Chari, On discrete Morse functions and combinatorial decompositions, Discrete Math. 217 (2000) 101 MR1766262
17 C C a Cheng, Separable semigroup algebras, J. Pure Appl. Algebra 33 (1984) 151 MR754952
18 F Chouraqui, Rewriting systems in alternating knot groups, Internat. J. Algebra Comput. 16 (2006) 749 MR2258837
19 D E Cohen, A monoid which is right FP but not left FP1, Bull. London Math. Soc. 24 (1992) 340 MR1165375
20 M M Cohen, A course in simple-homotopy theory, 10, Springer (1973) MR0362320
21 R Cremanns, F Otto, FP is undecidable for finitely presented monoids with word problems decidable in polynomial time, Universität Kassel (1998)
22 J F Davis, W Lück, Spaces over a category and assembly maps in isomorphism conjectures in K– and L–theory, K–Theory 15 (1998) 201 MR1659969
23 V Diekert, A J Duncan, A G Myasnikov, Geodesic rewriting systems and pregroups, from: "Combinatorial and geometric group theory" (editors O Bogopolski, I Bumagin, O Kharlampovich, E Ventura), Birkhäuser (2010) 55 MR2744016
24 E Dror Farjoun, A Zabrodsky, Homotopy equivalence between diagrams of spaces, J. Pure Appl. Algebra 41 (1986) 169 MR849903
25 S Eilenberg, T Ganea, On the Lusternik–Schnirelmann category of abstract groups, Ann. of Math. 65 (1957) 517 MR85510
26 D Farley, L Sabalka, Discrete Morse theory and graph braid groups, Algebr. Geom. Topol. 5 (2005) 1075 MR2171804
27 Z Fiedorowicz, Classifying spaces of topological monoids and categories, Amer. J. Math. 106 (1984) 301 MR737777
28 M G Fluch, M Marschler, S Witzel, M C B Zaremsky, The Brin–Thompson groups sV are of type F, Pacific J. Math. 266 (2013) 283 MR3130623
29 R Forman, A discrete Morse theory for cell complexes, from: "Geometry, topology, & physics" (editor S T Yau), International (1995) 112 MR1358614
30 R Forman, A user’s guide to discrete Morse theory, Sém. Lothar. Combin. 48 (2002) 35 MR1939695
31 R Freij, Equivariant discrete Morse theory, Discrete Math. 309 (2009) 3821 MR2537376
32 P Gabriel, M Zisman, Calculus of fractions and homotopy theory, 35, Springer (1967) MR0210125
33 R Geoghegan, Topological methods in group theory, 243, Springer (2008) MR2365352
34 O Goodman, M Shapiro, On a generalization of Dehn’s algorithm, Internat. J. Algebra Comput. 18 (2008) 1137 MR2468741
35 R D Gray, B Steinberg, Topological finiteness properties of monoids, II : special monoids, one-relator monoids, amalgamated free products, and HNN extensions, preprint (2018) arXiv:1805.03413
36 R D Gray, B Steinberg, Free inverse monoids are not FP2, C. R. Math. Acad. Sci. Paris 359 (2021) 1047 MR4323003
37 R D Gray, B Steinberg, A Lyndon’s identity theorem for one-relator monoids, Selecta Math. 28 (2022) 53 MR4414135
38 V S Guba, S J Pride, On the left and right cohomological dimension of monoids, Bull. London Math. Soc. 30 (1998) 391 MR1620825
39 V S Guba, M V Sapir, Diagram groups and directed 2–complexes : homotopy and homology, J. Pure Appl. Algebra 205 (2006) 1 MR2193190
40 Y Guiraud, P Malbos, Higher-dimensional normalisation strategies for acyclicity, Adv. Math. 231 (2012) 2294 MR2964639
41 S Hermiller, M Shapiro, Rewriting systems and geometric three-manifolds, Geom. Dedicata 76 (1999) 211 MR1703216
42 A Hess, V Ozornova, Factorability, string rewriting and discrete Morse theory, preprint (2014) arXiv:1412.3025
43 G Hochschild, On the cohomology groups of an associative algebra, Ann. of Math. 46 (1945) 58 MR11076
44 J M Howie, Embedding theorems for semigroups, Quart. J. Math. Oxford Ser. 14 (1963) 254 MR153764
45 J M Howie, Fundamentals of semigroup theory, 12, Oxford Univ. Press (1995) MR1455373
46 C M Hurwitz, On the homotopy theory of monoids, J. Austral. Math. Soc. Ser. A 47 (1989) 171 MR1008833
47 G Kalai, R Meshulam, A topological colorful Helly theorem, Adv. Math. 191 (2005) 305 MR2103215
48 D M Kan, W P Thurston, Every connected space has the homology of a K(π,1), Topology 15 (1976) 253 MR413089
49 U Knauer, Projectivity of acts and Morita equivalence of monoids, Semigroup Forum 3 (1971/72) 359 MR286914
50 Y Kobayashi, Every one-relation monoid has finite derivation type, from: "Proceedings of the Third Symposium on Algebra, Languages and Computation" (editor T Imaoka), Shimane Univ. (2000) 16 MR1774195
51 Y Kobayashi, Gröbner bases of associative algebras and the Hochschild cohomology, Trans. Amer. Math. Soc. 357 (2005) 1095 MR2110434
52 Y Kobayashi, The homological finiteness property FP1 and finite generation of monoids, Internat. J. Algebra Comput. 17 (2007) 593 MR2333373
53 Y Kobayashi, The homological finiteness properties left-, right-, and bi-FPn of monoids, Comm. Algebra 38 (2010) 3975 MR2764844
54 Y Kobayashi, F Otto, On homotopical and homological finiteness conditions for finitely presented monoids, Internat. J. Algebra Comput. 11 (2001) 391 MR1848788
55 T Y Lam, Lectures on modules and rings, 189, Springer (1999) MR1653294
56 I J Leary, B E A Nucinkis, Every CW–complex is a classifying space for proper bundles, Topology 40 (2001) 539 MR1838994
57 R C Lyndon, Cohomology theory of groups with a single defining relation, Ann. of Math. 52 (1950) 650 MR47046
58 R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR0577064
59 S Margolis, F Saliola, B Steinberg, Combinatorial topology and the global dimension of algebras arising in combinatorics, J. Eur. Math. Soc. 17 (2015) 3037 MR3429159
60 S Margolis, F V Saliola, B Steinberg, Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry, 1345, Amer. Math. Soc. (2021) MR4365944
61 J P May, Simplicial objects in algebraic topology, 11, Van Nostrand (1967) MR0222892
62 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
63 J P May, Classifying spaces and fibrations, 155, Amer. Math. Soc. (1975) MR370579
64 J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
65 J P May, A concise course in algebraic topology, University of Chicago Press (1999) MR1702278
66 D McDuff, On the classifying spaces of discrete monoids, Topology 18 (1979) 313 MR551013
67 D McDuff, G Segal, Homology fibrations and the “group-completion” theorem, Invent. Math. 31 (1976) 279 MR402733
68 J Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357 MR84138
69 B Mitchell, Rings with several objects, Advances in Math. 8 (1972) 1 MR294454
70 W R Nico, On the cohomology of finite semigroups, J. Algebra 11 (1969) 598 MR241505
71 P Nielsen, Can the trivial module be stably free for a monoid ring?, MathOverflow post (2016)
72 B V Novikov, Semigroups of cohomological dimension one, J. Algebra 204 (1998) 386 MR1624447
73 M Nunes, Cohomological results in monoid and category theory via classifying spaces, J. Pure Appl. Algebra 101 (1995) 213 MR1348037
74 E Pasku, On some homotopical and homological properties of monoid presentations, Semigroup Forum 76 (2008) 427 MR2395196
75 S J Pride, Homological finiteness conditions for groups, monoids, and algebras, Comm. Algebra 34 (2006) 3525 MR2260926
76 S J Pride, F Otto, For rewriting systems the topological finiteness conditions FDT and FHT are not equivalent, J. London Math. Soc. 69 (2004) 363 MR2040610
77 S J Pride, F Otto, On higher order homological finiteness of rewriting systems, J. Pure Appl. Algebra 200 (2005) 149 MR2142355
78 J Rhodes, B Tilson, The kernel of monoid morphisms, J. Pure Appl. Algebra 62 (1989) 227 MR1026876
79 J P Serre, Cohomologie des groupes discrets, from: "Prospects in mathematics", Ann. of Math. Studies 70, Princeton Univ. Press (1971) 77 MR0385006
80 C C Squier, Word problems and a homological finiteness condition for monoids, J. Pure Appl. Algebra 49 (1987) 201 MR920522
81 C C Squier, F Otto, Y Kobayashi, A finiteness condition for rewriting systems, Theoret. Comput. Sci. 131 (1994) 271 MR1288942
82 V Srinivas, Algebraic K–theory, , Birkhäuser (1996) MR2371852
83 J R Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968) 312 MR228573
84 R G Swan, Groups of cohomological dimension one, J. Algebra 12 (1969) 585 MR240177
85 C T C Wall, Finiteness conditions for CW–complexes, Ann. of Math. 81 (1965) 56 MR171284
86 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
87 C A Weibel, The K–book : an introduction to algebraic K–theory, 145, Amer. Math. Soc. (2013) MR3076731