Andrei Pajitnov

Circle-valued morse theory

In 1927, M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.

THE WHITEHEAD GROUP OF THE NOVIKOV RING

The Bass-Heller-Swan-Farrell-Hsiang-Siebenmann decomposition of the Whitehead group

Closed orbits of gradient flows and logarithms of non-abelian Witt vectors

K_1(A_{\rho}[z,z^{-1}])

Novikov homology, twisted Alexander polynomials and Thurston cones

of a twisted Laurent polynomial extension

Twisted Novikov homology and circle-valued Morse theory for knots and links

A_{\rho}[z,z^{-1}]

On the tunnel number and the Morse–Novikov number of knots

of a ring

On the Fixed Points of a Hamiltonian Diffeomorphism in Presence of Fundamental Group

A

Novikov homology, jump loci and Massey products

is generalized to a decomposition of the Whitehead group

ON THE ASYMPTOTICS OF MORSE NUMBERS OF FINITE COVERS OF MANIFOLDS

K_1(A_{\rho}((z)))

MORSE-NOVIKOV THEORY, HEEGAARD SPLITTINGS AND CLOSED ORBITS OF GRADIENT FLOWS

of a twisted Novikov ring of power series