Algebraic & Geometric Topology Volume 23, issue 9 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

A connection between cut locus, Thom space and Morse–Bott functions

Somnath Basu and Sachchidanand Prasad

Algebraic & Geometric Topology 23 (2023) 4185–4233

DOI: 10.2140/agt.2023.23.4185

Bibliography

1	A Banyaga, D Hurtubise, Lectures on Morse homology, 29, Kluwer Academic (2004) MR2145196
2	M G Barratt, J Milnor, An example of anomalous singular homology, Proc. Amer. Math. Soc. 13 (1962) 293 MR0137110
3	R L Bishop, R J Crittenden, Geometry of manifolds, XV, Academic (1964) MR169148
4	M A Buchner, Simplicial structure of the real analytic cut locus, Proc. Amer. Math. Soc. 64 (1977) 118 MR0474133
5	H Busemann, The geometry of geodesics, Academic (1955) MR0075623
6	A Daniilidis, R Deville, E Durand-Cartagena, L Rifford, Self-contracted curves in Riemannian manifolds, J. Math. Anal. Appl. 457 (2018) 1333 MR3705356
7	H Gluck, D Singer, Scattering of geodesic fields, I, Ann. of Math. 108 (1978) 347 MR0506991
8	A Gray, Tubes, 221, Birkhäuser (2004) MR2024928
9	J J Hebda, The local homology of cut loci in Riemannian manifolds, Tohoku Math. J. 35 (1983) 45 MR0695658
10	J J Hebda, Cut loci of submanifolds in space forms and in the geometries of Möbius and Lie, Geom. Dedicata 55 (1995) 75 MR1326741
11	N J Higham, Functions of matrices: theory and computation, Society for Industrial and Applied Mathematics (2008) MR2396439
12	M W Hirsch, Differential topology, 33, Springer (1994) MR1336822
13	J i Itoh, S V Sabau, Riemannian and Finslerian spheres with fractal cut loci, Differential Geom. Appl. 49 (2016) 43 MR3573823
14	J i Itoh, C Vîlcu, Orientable cut locus structures on graphs, preprint (2011) arXiv:1103.3136
15	J i Itoh, C Vîlcu, Every graph is a cut locus, J. Math. Soc. Japan 67 (2015) 1227 MR3376586
16	S Kobayashi, On conjugate and cut loci, from: "Studies in global geometry and analysis", Math. Assoc. America (1967) 96 MR0212737
17	Y Li, L Nirenberg, The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton–Jacobi equations, Comm. Pure Appl. Math. 58 (2005) 85 MR2094267
18	C Mantegazza, A C Mennucci, Hamilton–Jacobi equations and distance functions on Riemannian manifolds, Appl. Math. Optim. 47 (2003) 1 MR1941909
19	R J Martin, P Neff, Minimal geodesics on GL(n) for left-invariant, right-O(n)–invariant Riemannian metrics, J. Geom. Mech. 8 (2016) 323 MR3562278
20	S B Myers, Connections between differential geometry and topology, I : Simply connected surfaces, Duke Math. J. 1 (1935) 376 MR1545884
21	H Omori, A class of Riemannian metrics on a manifold, J. Differential Geometry 2 (1968) 233 MR0239625
22	S Plotnick, Embedding homology 3–spheres in S⁵, Pacific J. Math. 101 (1982) 147 MR0671847
23	H Poincaré, Sur les lignes géodésiques des surfaces convexes, Trans. Amer. Math. Soc. 6 (1905) 237 MR1500710
24	M M Postnikov, Geometry, VI : Riemannian geometry, 91, Springer (2001) MR1824853
25	S V Sabau, M Tanaka, The cut locus and distance function from a closed subset of a Finsler manifold, Houston J. Math. 42 (2016) 1157 MR3609822
26	T Sakai, Riemannian geometry, 149, Amer. Math. Soc. (1996) MR1390760
27	V A Sharafutdinov, Complete open manifolds of nonnegative curvature, Sibirsk. Mat. Zh. 15 (1974) 126 MR343208
28	H Singh, On the cut locus and the focal locus of a submanifold in a Riemannian manifold, II, Publ. Inst. Math. (Beograd) 41(55) (1987) 119 MR0919565
29	F E Wolter, Distance function and cut loci on a complete Riemannian manifold, Arch. Math. (Basel) 32 (1979) 92 MR0532854
30	V A Yakubovich, V M Starzhinskii, Linear differential equations with periodic coefficients, Halsted (1975) MR0364740