From Wikipedia, the free encyclopedia
In
mathematics, circle-valued Morse theory studies the topology of a
smooth manifold by analyzing the
critical points of smooth maps from the manifold to the
circle, in the framework of
Morse homology.
[1] It is an important special case of
Sergei Novikov's
Morse theory of closed
one-forms.
[2]
Michael Hutchings and Yi-Jen Lee have connected it to
Reidemeister torsion and
Seiberg–Witten theory.
[3]
References
-
^ Pajitnov, Andrei V. (2006), Circle-valued Morse theory, de Gruyter Studies in Mathematics, vol. 32, Walter de Gruyter & Co., Berlin,
doi:
10.1515/9783110197976,
ISBN
978-3-11-015807-6,
MR
2319639.
-
^ Farber, Michael (2004),
Topology of closed one-forms, Mathematical Surveys and Monographs, vol. 108, American Mathematical Society, Providence, RI, p. 50,
doi:
10.1090/surv/108,
ISBN
0-8218-3531-9,
MR
2034601.
-
^
Hutchings, Michael; Lee, Yi-Jen (1999), "Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds",
Topology, 38 (4): 861–888,
arXiv:
dg-ga/9612004,
doi:
10.1016/S0040-9383(98)00044-5,
MR
1679802,
S2CID
12740033.