In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using the smooth structure and an auxiliary metric on the manifold, but turns out to be topo ...
. It is an important special case of
Sergei Novikov's
Morse theory of closed
one-forms.
Michael Hutchings and Yi-Jen Lee have connected it to
Reidemeister torsion
In mathematics, Reidemeister torsion (or R-torsion, or Reidemeister–Franz torsion) is a topological invariant of manifolds introduced by Kurt Reidemeister for 3-manifolds and generalized to higher dimensions by and .
Analytic torsion (or Ray– ...
and
Seiberg–Witten theory
In theoretical physics, Seiberg–Witten theory is a theory that determines an exact low-energy effective action (for massless degrees of freedom) of a \mathcal = 2 supersymmetric gauge theory—namely the metric of the moduli space of vacua.
S ...
.
[.]
References
Morse theory
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