Home

Algebraic topology

Formal sciences
Mathematics
Topology
Algebraic topology

Related publications (30)

About
Privacy
Disclaimer

Graph Chatbot

The cohomology of semi-simple Lie groups, viewed from infinity

We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...

2022

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Computational tools for twisted topological Hochschild homology of equivariant spectra

Kathryn Hess Bellwald, Inbar Klang

Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we intr ...

ELSEVIER2022

Lamplighters and the bounded cohomology of Thompson's group

Nicolas Monod

We prove the vanishing of the bounded cohomology of lamplighter groups for a wide range of coefficients. This implies the same vanishing for a number of groups with self-similarity properties, such as Thompson's group F. In particular, these groups are bou ...

SPRINGER BASEL AG2022

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

A Künneth theorem for configuration spaces

Kathryn Hess Bellwald

We construct a spectral sequence converging to the homology of the ordered configuration spaces of a product of parallelizable manifolds. To identify the second page of this spectral sequence, we introduce a version of the Boardman-Vogt tensor product for ...

2022

Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

Oscar Salomon Kivinen

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...

WILEY2022

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

Axonal and Dendritic Morphology of Excitatory Neurons in Layer 2/3 Mouse Barrel Cortex Imaged Through Whole-Brain Two-Photon Tomography and Registered to a Digital Brain Atlas

Carl Petersen, Sylvain Crochet, Georgios Foustoukos, Yanqi Liu

Communication between cortical areas contributes importantly to sensory perception and cognition. On the millisecond time scale, information is signaled from one brain area to another by action potentials propagating across long-range axonal arborizations. ...

FRONTIERS MEDIA SA2022

Page 3 of 3

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

EPFL2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

Axonal and Dendritic Morphology of Excitatory Neurons in Layer 2/3 Mouse Barrel Cortex Imaged Through Whole-Brain Two-Photon Tomography and Registered to a Digital Brain Atlas

Carl Petersen, Sylvain Crochet, Georgios Foustoukos, Yanqi Liu

FRONTIERS MEDIA SA2022