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Concept

Homologie de Floer

Publications associées (23)

Short homology bases for hyperelliptic hyperbolic surfaces

Jürgpeter Buser

Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...

Hebrew Univ Magnes Press2023

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

Relative plus constructions

Jérôme Scherer

Let h be a connective homology theory. We construct a functorial relative plus construction as a Bousfield localization functor in the category of maps of spaces. It allows us to associate to a pair (X,H), consisting of a connected space X and an hperfect ...

2023

Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic

Jürgpeter Buser

We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...

2021

Instanton theory of ground-state tunneling splittings with general paths

Christophe Louis Joseph Jean-Luc Vaillant

We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem. Phys. 115, 6881 (2001)] to include asymmetric p ...

2020

Combinatorial presentation of multidimensional persistent homology

Martina Scolamiero

A multifiltration is a functor indexed by Nr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural Nr-graded R[x(1),...x(r)]-module structure on the homology of a multifiltration of ...

Elsevier2017

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

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

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 properties of nilpotent spaces

Jérôme Scherer

We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into classifying spaces of nilpotent groups. We use a modified Bousfield-Kan homology ...

Geometry & Topology Publications2015

From Compact Semi-Toric Systems To Hamiltonian S-1-Spaces

Silvia Sabatini

We show how any labeled convex polygon associated to a compact semi-toric system, as de fined by V (u) over tilde Ngoc, determines Karshon's labeled directed graph which classifies the underlying Hamiltonian S-1-space up to isomorphism. Then we characteriz ...

Amer Inst Mathematical Sciences2015

Higher Morse moduli spaces and n-categories

We generalize Cohen & Jones & Segal's flow category, whose objects are the critical points of a Morse function and whose morphisms are the Morse moduli spaces between the critical points to an n-category. The n-category construction involves repeatedly doi ...

Int Press Boston, Inc2014

Homoclinic Points And Floer Homology

A new relation between homoclinic points and Lagrangian Floer homology is presented: in dimension two, we construct a Floer homology generated by primary homoclinic points. We compute two examples and prove an invariance theorem. Moreover, we establish a l ...

Int Press Boston, Inc2013

Homotopy completion and topological Quillen homology of structured ring spectra

Kathryn Hess Bellwald

Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of modules over a commutative ring spectrum (eg structured ring spectra). We prove a strong convergenc ...

Geometry & Topology Publications2013

Transport, Flux And Growth Of Homoclinic Floer Homology

We point out an interesting relation between transport in Hamiltonian dynamics and Floer homology. We generalize homoclinic Floer homology from R-2 and closed surfaces to two-dimensional cylinders. The relative symplectic action of two homoclinic points is ...

Amer Inst Mathematical Sciences2012

Ideal knots and other packing problems of tubes

This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...

EPFL2010

Computation and visualization of ideal knot shapes

We investigate numerical simulations and visualizations of the problem of tying a knot in a piece of rope. The goal is to use the least possible rope of a fixed, prescribed radius to tie a particular knot, e.g. a trefoil, a figure eight, and so on. The rop ...

EPFL2010

Poisson Reduction by Distributions

Tudor Ratiu, Madeleine Jotz

It is shown that the singular Poisson reduction procedure can be improved for a large class of situations. In addition, Poisson reduction of orbit type manifolds is carried out in detail. ...

Springer Verlag2009

Stable classical groups and strongly torsion generated groups

Strongly torsion generated groups are those with a single normal generator, of arbitrary finite order. They are useful for realizing sequences of abelian groups as homology groups. Known examples include stable alternating groups and stable groups generate ...

2009

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Jean Fasel

Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d

2009

Publications associées (23)

Springer Verlag2009

Stable classical groups and strongly torsion generated groups

2009

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Jean Fasel

2009