Algebraic & Geometric Topology Volume 18, issue 7 (2018)

Download this article
	For screen
	For printing

Recent 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

Cohomology of symplectic groups and Meyer's signature theorem

Dave Benson, Caterina Campagnolo, Andrew Ranicki and Carmen Rovi

Algebraic & Geometric Topology 18 (2018) 4069–4091

DOI: 10.2140/agt.2018.18.4069

Bibliography

1	H Behr, Explizite Präsentation von Chevalley-gruppen über Z, Math. Z. 141 (1975) 235 MR0422442
2	D J Benson, Theta functions and a presentation of 2^1+(2g+1)Sp(2g,2), preprint (2017)
3	S Bouc, N Mazza, The Dade group of (almost) extraspecial p–groups, J. Pure Appl. Algebra 192 (2004) 21 MR2067187
4	J F Carlson, J Thévenaz, Torsion endo-trivial modules, Algebr. Represent. Theory 3 (2000) 303 MR1808129
5	J H Conway, R T Curtis, S P Norton, R A Parker, R A Wilson, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups, Oxford Univ. Press (1985) MR827219
6	P Deligne, Extensions centrales non résiduellement finies de groupes arithmétiques, C. R. Acad. Sci. Paris Sér. A-B 287 (1978) MR507760
7	U Dempwolff, Extensions of elementary abelian groups of order 2²ⁿ by S_2n(2) and the degree 2–cohomology of S_2n(2), Illinois J. Math. 18 (1974) 451 MR0348004
8	P Diaconis, Threads through group theory, from: "Character theory of finite groups" (editors M L Lewis, G Navarro, D S Passman, T R Wolf), Contemp. Math. 524, Amer. Math. Soc. (2010) 33 MR2731916
9	C J Earle, J Eells, A fibre bundle description of Teichmüller theory, J. Differential Geometry 3 (1969) 19 MR0276999
10	H Endo, A construction of surface bundles over surfaces with non-zero signature, Osaka J. Math. 35 (1998) 915 MR1659565
11	L Funar, W Pitsch, Finite quotients of symplectic groups vs mapping class groups, preprint (2016)
12	S P Glasby, On the faithful representations, of degree 2ⁿ, of certain extensions of 2–groups by orthogonal and symplectic groups, J. Austral. Math. Soc. Ser. A 58 (1995) 232 MR1323995
13	T Gocho, The topological invariant of three-manifolds based on the U(1) gauge theory, Proc. Japan Acad. Ser. A Math. Sci. 66 (1990) 237 MR1077604
14	T Gocho, The topological invariant of three-manifolds based on the U(1) gauge theory, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 39 (1992) 169 MR1157982
15	D Gorenstein, Finite groups, Harper & Row (1968) MR0231903
16	R L Griess Jr., Automorphisms of extra special groups and nonvanishing degree 2 cohomology, Pacific J. Math. 48 (1973) 403 MR0476878
17	P Hall, G Higman, On the p–length of p–soluble groups and reduction theorems for Burnside’s problem, Proc. London Math. Soc. 6 (1956) 1 MR0072872
18	I Hambleton, A Korzeniewski, A Ranicki, The signature of a fibre bundle is multiplicative mod 4, Geom. Topol. 11 (2007) 251 MR2302493
19	M E Hamstrom, Homotopy groups of the space of homeomorphisms on a 2–manifold, Illinois J. Math. 10 (1966) 563 MR0202140
20	G Hiss, Die adjungierten Darstellungen der Chevalley–Gruppen, Arch. Math. (Basel) 42 (1984) 408 MR756692
21	B Huppert, Endliche Gruppen, I, 134, Springer (1967) MR0224703
22	J i Igusa, On the graded ring of theta-constants, Amer. J. Math. 86 (1964) 219 MR0164967
23	A Korzeniewski, On the signature of fibre bundles and absolute Whitehead torsion, PhD thesis, University of Edinburgh (2005)
24	T Y Lam, T Smith, On the Clifford–Littlewood–Eckmann groups : a new look at periodicity mod 8, Rocky Mountain J. Math. 19 (1989) 749 MR1043247
25	R Luke, W K Mason, The space of homeomorphisms on a compact two-manifold is an absolute neighborhood retract, Trans. Amer. Math. Soc. 164 (1972) 275 MR0301693
26	W Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973) 239 MR0331382
27	G Nebe, E M Rains, N J A Sloane, The invariants of the Clifford groups, Des. Codes Cryptogr. 24 (2001) 99 MR1845897
28	M Newman, J R Smart, Symplectic modulary groups, Acta Arith. 9 (1964) 83 MR0162862
29	A Putman, The Picard group of the moduli space of curves with level structures, Duke Math. J. 161 (2012) 623 MR2891531
30	D Quillen, The mod 2 cohomology rings of extra-special 2–groups and the spinor groups, Math. Ann. 194 (1971) 197 MR0290401
31	C Rovi, The nonmultiplicativity of the signature modulo 8 of a fibre bundle is an Arf–Kervaire invariant, Algebr. Geom. Topol. 18 (2018) 1281 MR3784006
32	B Runge, On Siegel modular forms, I, J. Reine Angew. Math. 436 (1993) 57 MR1207281
33	B Runge, On Siegel modular forms, II, Nagoya Math. J. 138 (1995) 179 MR1339948
34	B Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996) 175 MR1368288
35	M Sato, The abelianization of the level d mapping class group, J. Topol. 3 (2010) 847 MR2746340
36	P Schmid, On the automorphism group of extraspecial 2–groups, J. Algebra 234 (2000) 492 MR1800739
37	R Stancu, Almost all generalized extraspecial p–groups are resistant, J. Algebra 249 (2002) 120 MR1887988
38	M R Stein, Generators, relations and coverings of Chevalley groups over commutative rings, Amer. J. Math. 93 (1971) 965 MR0322073
39	M R Stein, The Schur multipliers of Sp₆(ℤ), Spin₈(ℤ), Spin₇(ℤ), and F₄(ℤ), Math. Ann. 215 (1975) 165 MR0372056
40	R Steinberg, Generators, relations and coverings of algebraic groups, II, J. Algebra 71 (1981) 527 MR630615
41	K Tsushima, On a decomposition of Bruhat type for a certain finite group, Tsukuba J. Math. 27 (2003) 307 MR2025730