Geometry & Topology Volume 19, issue 3 (2015)

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ISSN 1364-0380 (online)

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Geodesics and horizontal-path spaces in Carnot groups

Andrei A Agrachev, Alessandro Gentile and Antonio Lerario

Geometry & Topology 19 (2015) 1569–1630

DOI: 10.2140/gt.2015.19.1569

Bibliography

1	A A Agrachëv, The topology of quadratic mappings and Hessians of smooth mappings, from: "Algebra, Topology, Geometry" (editor R V Gamkrelidze), Itogi Nauki i Tekhniki 26, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform. (1988) 85, 162 MR978394
2	A A Agrachëv, U Boscain, D Barilari, Introduction to Riemannian and sub-Riemannian geometry (2015)
3	A A Agrachëv, A Lerario, Systems of quadratic inequalities, Proc. Lond. Math. Soc. 105 (2012) 622 MR2974201
4	J Bochnak, M Coste, M F Roy, Real algebraic geometry, Ergeb. Math. Grenzgeb. 36, Springer (1998) MR1659509
5	U Boscain, J P Gauthier, On the spherical Hausdorff measure in step $2$ corank–$2$ sub-Riemannian geometry, SIAM J. Control Optim. 51 (2013) 4450 MR3141746
6	R Bott, Nondegenerate critical manifolds, Ann. of Math. 60 (1954) 248 MR0064399
7	R Bott, Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. 7 (1982) 331 MR663786
8	K c Chang, Infinite-dimensional Morse theory and multiple solution problems, Progr. Nonlinear Diff. Eq. Appl. 6, Birkhäuser (1993) MR1196690
9	Z Ge, Horizontal path spaces and Carnot–Carathéodory metrics, Pacific J. Math. 161 (1993) 255 MR1242199
10	T Kato, Perturbation theory for linear operators, Classics in Math., Springer (1995) MR1335452
11	W Klingenberg, Lectures on closed geodesics, Ergeb. Math. Grenzgeb. 230, Springer (1978) MR0478069
12	A Lerario, Complexity of intersection of real quadrics and topology of symmetric determinantal varieties, to appear in J. of the Eur. Math. Soc.
13	A Lerario, Convex pencils of real quadratic forms, Discrete Comput. Geom. 48 (2012) 1025 MR3000573
14	J Milnor, Morse theory, Annals of Math. Studies 51, Princeton Univ. Press (1963) MR0163331
15	A L Onishchik, È B Vinberg, Lie groups and algebraic groups, Springer Series in Soviet Math., Springer (1990) MR1064110
16	P Pansu, Métriques de Carnot–Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. 129 (1989) 1 MR979599
17	S Semmes, An introduction to Heisenberg groups in analysis and geometry, Notices Amer. Math. Soc. 50 (2003) 640 MR1988576