175 citations · 459 across the 17 of their papers we have counts for
10 papers · 1 filter
The geometric cobordism hypothesis
Daniel Grady, Dmitri Pavlov
We prove a generalization of the cobordism hypothesis of Baez--Dolan and Hopkins--Lurie for bordisms with arbitrary geometric structures, such as Riemannian metrics, complex and sy…
Extended field theories are local and have classifying spaces
Daniel Grady, Dmitri Pavlov
We show that all extended functorial field theories, both topological and nontopological, are local. We define the smooth (infinity,d)-category of bordisms with geometric data, suc…
Twisted differential KO-theory
Daniel Grady, Hisham Sati
We provide a systematic approach to twisting differential KO-theory leading to a construction of the corresponding twisted differential Atiyah-Hirzebruch spectral sequence (AHSS).…
Cobordisms of global quotient orbifolds and an equivariant Pontrjagin-Thom construction
Daniel Grady
We introduce an equivariant Pontrjagin-Thom construction which identifies equivariant cohomotopy classes with certain fixed point bordism classes. This provides a concrete geometri…
Differential KO-theory: constructions, computations, and applications
Daniel Grady, Hisham Sati
We provide several constructions in differential KO-theory. First, we construct a differential refinement of the -genus and a pushforward leading to a Riemann-Roch theorem…
Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
Daniel Grady, Hisham Sati
We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' correspon…
Parametrized geometric cobordism and smooth Thom stacks
Daniel Grady, Hisham Sati
We develop a theory of parametrized geometric cobordism by introducing smooth Thom stacks. This requires identifying and constructing a smooth representative of the Thom functor ac…
Spectral sequences in smooth generalized cohomology
Daniel Grady, Hisham Sati
We consider spectral sequences in smooth generalized cohomology theories, including differential generalized cohomology theories. The main differential spectral sequences will be o…
Primary operations in differential cohomology
Daniel Grady, Hisham Sati
We characterize primary operations in differential cohomology via stacks, and illustrate by differentially refining Steenrod squares and Steenrod powers explicitly. This requires a…
Massey products in differential cohomology via stacks
Daniel Grady, Hisham Sati
We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties a…