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Chromatic Number of the Plane Meets Map Coloring: Townsend–Woodall’s 5-Color Theorem
In Chapter 8 , I described Douglas R. Woodall’s 1973 attempt to obtain a result on chromatic number of the...
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The Gauss Map of a Minimal Surface
In this chapter we continue and substantially expand the study of the Gauss map of minimal surfaces. The main new result of this chapter is that...
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The Abel map for surface singularities III: Elliptic germs
The present note is part of a series of articles targeting the theory of Abel maps associated with complex normal surface singularities with rational...
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Algebras with a negation map
In tropical mathematics, as well as other mathematical theories involving semirings, one often is challenged by the lack of negation when trying to...
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Local Regularity for the Harmonic Map and Yang–Mills Heat Flows
We establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 and 4,...
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The Igusa Quartic and the Prym Map, with Some Rational Moduli
This paper is devoted to the ubiquity of the Igusa quartic $$ B \,\subset...
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Virtual homological eigenvalues and the Weil-Petersson translation length
For any pseudo-Anosov automorphism on an orientable closed surface, an inequality is established by bounding certain growth of virtual homological...
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Coverings in the Category of Principal Bundles
We investigate the category of regular coverings of a given smooth principal bundle. A covering map of one principal bundle to another principal...
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Generalised Heegner cycles and the complex Abel–Jacobi map
Generalised Heegner cycles were introduced in Bertolini et al. (Duke Math J 162(6), 1033–1148, 2013) as a variant of Heegner cycles on Kuga–Sato...
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Codimension 2 transfer of higher index invariants
This paper is devoted to the study of the higher index theory of codimension 2 submanifolds originated by Gromov–Lawson and Hanke–Pape–Schick. The...
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Finite Time Blow-up for Heat Flows of Self-induced Harmonic Maps
Let M n be an embedded closed submanifold of ℝ k +1 or a smooth bounded domain in ℝ n , where n ≥ 3. We show that the local smooth solution to the heat...
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The Geometric Surgery Obstruction Group and Surgery Obstruction
This chapter is the equivalent to Chapter 9 inWall’s book [414].We give a geometric approach to the L-groups and the surgery obstruction based on...
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Perturbations of Nonhyperbolic Algebraic Automorphisms of the 2-Torus
AbstractAll nonhyperbolic automorphisms of the 2-torus are not structurally stable, and it is generally impossible to predict the dynamics of their...
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General birationality and hyperelliptic theta divisors
We first state a condition ensuring that having a birational map onto the image is an open property for families of irreducible normal non uniruled...
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The Liouville current of holomorphic quadratic differential metrics
In this paper we study the Liouville current of flat cone metrics coming from a holomorphic quadratic differential. Anja Bankovic and Christopher J....
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An averaging formula for Nielsen numbers on infra-solvmanifolds
Until now only for special classes of infra-solvmanifolds, namely, infra-nilmanifolds and infra-solvmanifolds of type ( R ), there was a formula...
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The relatively perfect Greenberg transform and cycle class maps
Given a scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field, the Greenberg transform produces a new...
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The Categorical Basis of Dynamical Entropy
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical...
