David Schrittesser's Books

The authors prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a $Delta^1_3$ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.

We develop diﬀerential algebraic K-theory for rings of integers in number ﬁelds and we construct a cycle map from geometrized bundles of modules over such a ring to the diﬀerential algebraic K-theory. We also treat some of the foundational aspects of diﬀerential cohomology, including diﬀerential function spectra and the diﬀerential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer deﬁned by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.

Manifolds with ﬁbered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coeﬃcients in a ﬂat bundle on a closed manifold undergoing degeneration to a manifold with ﬁbered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with ﬁbered cusps in terms of the R-torsion of the underlying manifold with boundary.

Book's by David Schrittesser

Projective Measure Without Projective Baire

Projective Measure Without Projective Baire

Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory

Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory

Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps

Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps

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