Geodesic
On the space of symmetric operators with multiple ground states
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 1-15

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We study the homology structure of the filtration of the space of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting on a finite-dimensional complex or real Hilbert space, but infinite-dimensional generalizations are easy to guess.
Keywords: self-adjoint operator, multiple eigenvalue, exact sequence. 
@article{FAA_2011_45_4_a0,
     author = {A. A. Agrachev},
     title = {On the space of symmetric operators with multiple ground states},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {1--15},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a0/}
}
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A. A. Agrachev. On the space of symmetric operators with multiple ground states. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 4, pp. 1-15. http://geodesic.mathdoc.fr/item/FAA_2011_45_4_a0/