Other kinds of contact and Floer homology
 Floer homology of families I
Geometric Topology 8 (2008), 435-492. Download. Erratum.
Abstract: In principle, Floer theory can be extended to define
homotopy invariants of families of equivalent objects
(e.g. Hamiltonian isotopic symplectomorphisms, 3-manifolds, 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 finite-dimensional Morse homology, and
shows that it recovers the Leray-Serre spectral sequence of a smooth
fiber bundle. We also generalize from Morse homology to Novikov
homology, which involves some additional subtleties.
 Cylindrical contact homology for dynamically convex contact forms in three dimensions (with J. Nelson),
Journal of Symplectic Geometry 14 (2016), 983-1012. Almost final version at arxiv:1407.2898. blog post
 Symplectic capacities from positive S^1-equivariant symplectic homology (with J. Gutt),
 Axiomatic S^1 Morse-Bott theory (with J. Nelson),
Up to Michael Hutchings's home page.