Geometric topology

Related publications (187)

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Eigenfunction Expansions Of Ultradifferentiable Functions And Ultradistributions

Aparajita Dasgupta

In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. Th ...

American Mathematical Society2016

Waldhausen K-theory of spaces via comodules

Kathryn Hess Bellwald

Let X be a simplicial set. We construct a novel adjunction be- tween the categories RX of retractive spaces over X and ComodX+ of X+- comodules, then apply recent work on left-induced model category structures [5], [16] to establish the existence of a left ...

Academic Press Inc Elsevier Science2016

Cellular Homotopy Excision

Kay Remo Werndli

There is a classical "duality" between homotopy and homology groups in that homotopy groups are compatible with homotopy pullbacks (every homotopy pullback gives rise to a long exact sequence in homotopy), while homology groups are compatible with homotopy ...

EPFL2016

Principal component component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids

Katharine Felicity Turner

Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the persistent homology rank functi ...

Elsevier2016

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

Aparajita Dasgupta

In this paper we give a global characterisation of classes of ultradi_erentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. Thi ...

2016

On a Lagrangian Formulation of the Incompressible Euler Equation

Hasan Inci

In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...

Global Science Press2016

Cohomological Hall algebras and character varieties

In this paper, we investigate the relationship between twisted and untwisted character varieties, via a specific instance of the Cohomological Hall algebra for moduli of objects in 3-Calabi-Yau categories introduced by Kontsevich and Soibelman. In terms of ...

World Scientific Publ Co Pte Ltd2016

Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis

We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to q ...

American Physical Society2015

MATHICSE Technical Report : A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media

Assyr Abdulle, Ondrej Budác

A reduced basis Darcy-Stokes finite element heterogeneous multiscale method (RB-DS-FE-HMM) is proposed for the Stokes problem in porous media. The multiscale method is based on the Darcy-Stokes finite element heterogeneous multiscale method (DS-FE-HMM) int ...

MATHICSE2015

Amenable hyperbolic groups

Nicolas Monod

We give a complete characterization of the locally compact groups that are nonelementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover gi ...

European Mathematical Soc2015