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1
D Abramovich , L
Caporaso , S Payne , The tropicalization of
the moduli space of curves , Ann. Sci. Éc. Norm. Supér.
48 (2015) 765 MR3377065
2
V Alexeev , A
Brunyate , Extending the
Torelli map to toroidal compactifications of Siegel
space , Invent. Math. 188 (2012) 175 MR2897696
3
D Allcock , D
Corey , S Payne , Tropical moduli spaces as
symmetric Δ –complexes ,
Bull. Lond. Math. Soc. 54 (2022) 193 MR4396931
4
A Ash , D
Mumford , M Rapoport , Y Tai , Smooth
compactification of locally symmetric varieties , 4, Math.
Sci. Press (1975) MR0457437
5
W L Baily Jr. ,
A Borel , Compactification of
arithmetic quotients of bounded symmetric domains , Ann.
of Math. 84 (1966) 442 MR0216035
6
A Borel , Stable real cohomology of
arithmetic groups , Ann. Sci. École Norm. Sup. 7 (1974)
235 MR0387496
7
A Borel , J P
Serre , Corners and arithmetic
groups , Comment. Math. Helv. 48 (1973) 436 MR0387495
8
S Brannetti , M
Melo , F Viviani , On the tropical
Torelli map , Adv. Math. 226 (2011) 2546 MR2739784
9
F Brown , Mixed Tate
motives over ℤ , Ann. of
Math. 175 (2012) 949 MR2993755
10
B Brück , J
Miller , P Patzt , R J Sroka ,
J C H Wilson , On the codimension-two
cohomology of SL n ( ℤ ) , preprint (2022) arXiv:2204.11967
11
M Chan , Combinatorics of the
tropical Torelli map , Algebra Number Theory 6 (2012)
1133 MR2968636
12
M Chan , S
Galatius , S Payne , Tropical curves, graph
complexes, and top weight cohomology of ℳ g , J. Amer. Math. Soc. 34 (2021)
565 MR4280867
13
M Chan , M Melo ,
F Viviani , Tropical Teichmüller
and Siegel spaces , from: "Algebraic and combinatorial
aspects of tropical geometry" (editors E Brugallé, M A
Cueto, A Dickenstein, E M Feichtner, I Itenberg), Contemp.
Math. 589, Amer. Math. Soc. (2013) 45 MR3088910
14
R Charney , R
Lee , Cohomology of
the Satake compactification , Topology 22 (1983) 389
MR0715247
15
J Chen , E
Looijenga , The stable cohomology
of the Satake compactification of 𝒜 g , Geom. Topol. 21 (2017) 2231
MR3654107
16
T Church , B
Farb , A Putman , A stability conjecture
for the unstable cohomology of SL n ℤ , mapping
class groups, and Aut ( F n ) ,
from: "Algebraic topology: applications and new directions"
(editors U Tillmann, S r Galatius, D Sinha), Contemp.
Math. 620, Amer. Math. Soc. (2014) 55 MR3290086
17
T Church , A
Putman , The codimension-one
cohomology of SL n ℤ ,
Geom. Topol. 21 (2017) 999 MR3626596
18
D A Cox ,
J B Little , H K Schenck , Toric varieties , 124,
Amer. Math. Soc. (2011) MR2810322
19
P Deligne , Théorie de Hodge,
II , Inst. Hautes Études Sci. Publ. Math. 40 (1971) 5
MR0498551
20
P Deligne , Théorie de Hodge,
III , Inst. Hautes Études Sci. Publ. Math. 44 (1974) 5
MR0498552
21
M Dutour Sikirić , P
Elbaz-Vincent , A Kupers , J Martinet ,
Voronoi complexes in higher dimensions, cohomology of
GL N ( Z ) for N
≥ 8
and the triviality of K 8 ( Z ) , preprint
(2019) arXiv:1910.11598
22
P Elbaz-Vincent , H
Gangl , C Soulé , Perfect forms,
K–theory and the cohomology of modular groups , Adv.
Math. 245 (2013) 587 MR3084439
23
G Faltings ,
C L Chai , Degeneration of
abelian varieties , 22, Springer (1990) MR1083353
24
S Grushevsky ,
Geometry of
𝒜 g and its compactifications ,
from: "Algebraic geometry, I" (editors D Abramovich, A Bertram,
L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure
Math. 80.1, Amer. Math. Soc. (2009) 193 MR2483936
25
S Grushevsky , K
Hulek , O Tommasi , Stable
Betti numbers of (partial) toroidal compactifications of the
moduli space of abelian varieties , from: "Geometry and
physics, II" (editors J E Andersen, A Dancer, O
García-Prada), Oxford Univ. Press (2018) 581 MR3931788
26
S Grushevsky , K
Hulek , O Tommasi , Stable cohomology of
the perfect cone toroidal compactification of 𝒜 g , J. Reine Angew. Math. 741
(2018) 211 MR3836148
27
R Hain , The rational
cohomology ring of the moduli space of abelian 3 –folds , Math. Res. Lett. 9 (2002) 473
MR1928867
28
F Harary , M J
Piff , D J A Welsh , On the
automorphism group of a matroid , Discrete Math. 2
(1972) 163 MR0297639
29
G Harder , A Gauss–Bonnet formula
for discrete arithmetically defined groups , Ann. Sci.
École Norm. Sup. 4 (1971) 409 MR0309145
30
A Hatcher , Algebraic
topology , Cambridge Univ. Press (2002) MR1867354
31
K Hulek , O
Tommasi , Cohomology of the second
Voronoi compactification of 𝒜 4 , Doc. Math. 17 (2012) 195
MR2946823
32
K Hulek , O
Tommasi , The topology of
𝒜 g and its compactifications ,
from: "Geometry of moduli" (editors J A Christophersen, K
Ranestad), Abel Symp. 14, Springer (2018) 135 MR3968046
33
J Igusa , On Siegel modular forms of
genus two , Amer. J. Math. 84 (1962) 175 MR0141643
34
D O
Jaquet-Chiffelle , Énumération complète des
classes de formes parfaites en dimension 7 , Ann. Inst. Fourier (Grenoble) 43
(1993) 21 MR1209694
35
R Lee , R H
Szczarba , On the homology and
cohomology of congruence subgroups , Invent. Math. 33
(1976) 15 MR0422498
36
R Lee , R H
Szczarba , On the torsion
in K 4 ( ℤ ) and
K 5 ( ℤ ) , Duke
Math. J. 45 (1978) 101 MR0491893
37
M Melo , F
Viviani , Comparing perfect
and 2nd Voronoi decompositions : the matroidal locus ,
Math. Ann. 354 (2012) 1521 MR2993003
38
Y Namikawa ,
Toroidal
compactification of Siegel spaces , 812, Springer (1980)
MR0584625
39
Y Odaka , Tropical geometric
compactification of moduli, II : A g case
and holomorphic limits , Int. Math. Res. Not. 2019
(2019) 6614 MR4027562
40
Y Odaka , Y
Oshima , Collapsing K3 surfaces, tropical
geometry and moduli compactifications of Satake, Morgan–Shalen
type , 40, Math. Soc. Japan (2021) MR4290084
41
J G Oxley ,
Matroid
theory , Oxford Univ. Press (1992) MR1207587
42
N I
Shepherd-Barron , Perfect forms and
the moduli space of abelian varieties , Invent. Math.
163 (2006) 25 MR2208417
43
C Soulé , On the
3 –torsion in K 4 ( ℤ ) ,
Topology 39 (2000) 259 MR1722032
44
G Voronoi , Nouvelles
applications des paramètres continus à la théorie des formes
quadratiques, I : Sur quelques propriétés des formes
quadratiques positives parfaites , J. Reine Angew. Math.
133 (1908) 97 MR1580737
45
H Whitney , Congruent graphs and the
connectivity of graphs , Amer. J. Math. 54 (1932) 150
MR1506881
46
T Willwacher ,
M
Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie
algebra , Invent. Math. 200 (2015) 671 MR3348138