Algebraic & Geometric Topology Volume 24, issue 4 (2024)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Moduli spaces of geometric graphs

Mara Belotti, Antonio Lerario and Andrew Newman

Algebraic & Geometric Topology 24 (2024) 2039–2090

DOI: 10.2140/agt.2024.24.2039

Bibliography

1	A Abbondandolo, A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces, Topol. Methods Nonlinear Anal. 9 (1997) 325 MR1491851
2	A A Agrachëv, Homology of the intersections of real quadrics, Dokl. Akad. Nauk SSSR 299 (1988) 1033 MR0947225
3	A A Agrachëv, The topology of quadratic mappings and Hessians of smooth mappings, Algebra, Topol. Geom. 26 (1988) 85 MR0978394
4	A A Agrachëv, A Gentile, A Lerario, Geodesics and horizontal-path spaces in Carnot groups, Geom. Topol. 19 (2015) 1569 MR3352244
5	A Agrachëv, A Lerario, Systems of quadratic inequalities, Proc. Lond. Math. Soc. 105 (2012) 622 MR2974201
6	A Auffinger, A Lerario, E Lundberg, Topologies of random geometric complexes on Riemannian manifolds in the thermodynamic limit, Int. Math. Res. Not. 2021 (2021) 15497 MR4329874
7	S Basu, Different bounds on the different Betti numbers of semi-algebraic sets, Discrete Comput. Geom. 30 (2003) 65 MR1991587
8	A Björner, Nerves, fibers and homotopy groups, J. Combin. Theory Ser. A 102 (2003) 88 MR1970978
9	J Bochnak, M Coste, M F Roy, Real algebraic geometry, 36, Springer (1998) MR1659509
10	M Dyer, C Greenhill, The complexity of counting graph homomorphisms, Random Structures Algorithms 17 (2000) 260 MR1801135
11	E R Fadell, S Y Husseini, Geometry and topology of configuration spaces, Springer (2001) MR1802644
12	P Flajolet, R Sedgewick, Analytic combinatorics, Cambridge Univ. Press (2009) MR2483235
13	K Gęba, A Granas, Infinite dimensional cohomology theories, J. Math. Pures Appl. 52 (1973) 145 MR0380865
14	M Gutierrez, L Oubiña, Metric characterizations of proper interval graphs and tree-clique graphs, J. Graph Theory 21 (1996) 199 MR1368745
15	P Hanlon, Counting interval graphs, Trans. Amer. Math. Soc. 272 (1982) 383 MR0662044
16	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
17	P Hell, J Nesetril, On the complexity of H–coloring, J. Combin. Theory Ser. B 48 (1990) 92 MR1047555
18	M W Hirsch, Differential topology, 33, Springer (1976) MR448362
19	Z Jackowski, A new characterization of proper interval graphs, Discrete Math. 105 (1992) 103 MR1180196
20	R J Kang, T Müller, Sphere and dot product representations of graphs, Discrete Comput. Geom. 47 (2012) 548 MR2891247
21	C G Lekkerkerker, J C Boland, Representation of a finite graph by a set of intervals on the real line, Fund. Math. 51 (1962) 45 MR0139159
22	A Lerario, Homology invariants of quadratic maps, PhD thesis, SISSA (2011)
23	H Maehara, Space graphs and sphericity, Discrete Appl. Math. 7 (1984) 55 MR0722183
24	C McDiarmid, T Müller, The number of disk graphs, European J. Combin. 35 (2014) 413 MR3090514
25	G B Mertzios, A matrix characterization of interval and proper interval graphs, Appl. Math. Lett. 21 (2008) 332 MR2406509
26	J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR0163331
27	J Milnor, On the Betti numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964) 275 MR0161339
28	J W Milnor, J D Stasheff, Characteristic classes, 76, Princeton Univ. Press (1974) MR0440554
29	F S Roberts, Indifference graphs, from: "Proof techniques in graph theory" (editor F Harary), Academic (1969) 139 MR0252267
30	R P Stanley, An introduction to hyperplane arrangements, from: "Geometric combinatorics" (editors E Miller, V Reiner, B Sturmfels), IAS/Park City Math. Ser. 13, Amer. Math. Soc. (2007) 389 MR2383131
31	A Szulkin, Cohomology and Morse theory for strongly indefinite functionals, Math. Z. 209 (1992) 375 MR1152264
32	H E Warren, Lower bounds for approximation by nonlinear manifolds, Trans. Amer. Math. Soc. 133 (1968) 167 MR0226281