This text features a careful treatment of flow lines and
algebraic invariants in contact form geometry, a vast area of
research connected to symplectic field theory, pseudo-holomorphic
curves, and Gromov-Witten invariants (contact homology). In
particular, it develops a novel algebraic tool in this field:
rooted in the concept of critical points at infinity, the new
algebraic invariants defined here are useful in the investigation
of contact structures and Reeb vector fields. The book opens with a
review of prior results and then proceeds through an examination of
variational problems, non-Fredholm behavior, true and false
critical points at infinity, and topological implications. An
increasing convergence with regular and singular Yamabe-type
problems is discussed, and the intersection between contact form
and Riemannian geometry is emphasized. Rich in open problems and
full, detailed proofs, this work lays the foundation for new
avenues of study in contact form geometry and will benefit graduate
students and researchers.
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