Other kinds of contact and Floer homology

[1] Floer homology of families I
Algebraic and
Geometric Topology 8 (2008), 435492. Download. Erratum.
Abstract: In principle, Floer theory can be extended to define
homotopy invariants of families of equivalent objects
(e.g. Hamiltonian isotopic symplectomorphisms, 3manifolds, Legendrian
knots, etc.) parametrized by a smooth manifold B. The invariant of a
family consists of a filtered chain homotopy type, which gives rise to
a spectral sequence whose E^2 term is the homology of B with twisted
coefficients in the Floer homology of the fibers. This filtered chain
homotopy type also gives rise to a "family Floer homology" to which
the spectral sequence converges. For any particular version of Floer
theory, some analysis needs to be carried out in order to turn this
principle into a theorem. This paper constructs the spectral sequence
in detail for the model case of finitedimensional Morse homology, and
shows that it recovers the LeraySerre spectral sequence of a smooth
fiber bundle. We also generalize from Morse homology to Novikov
homology, which involves some additional subtleties.

[2] Cylindrical contact homology for dynamically convex contact forms in three dimensions (with J. Nelson),
Journal of Symplectic Geometry 14 (2016), 9831012. Almost final version at arxiv:1407.2898. blog post

[3] Symplectic capacities from positive S^1equivariant symplectic homology (with J. Gutt),
arXiv:1707.06514.

[4] Axiomatic S^1 MorseBott theory (with J. Nelson),
arXiv:1711.09996.
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