In \cite{GrOrang}, Gromov asks the following question: given a nullhomotopic map of Lipschitz constant , how does the Lipschitz constant of an optimal nullhomotopy of depend on , , and ? We establish that for fixed and , the answer is at worst quadratic in . More precisely, we …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
7 results for “nullhomotopy”
Upper bounds on nullhomotopy volumes in nilpotent spaces are refined.
problem Bounding volumes of nullhomotopies in nilpotent spaces.
method Extension of the Shadowing Principle to nilpotent spaces.
result Improved bounds on nullhomotopy volumes, nearly meeting simply connected settings.
It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a based nullhomotopy of the double-twist loop in the special orthogonal group of rotations. We study a particularly simple, …
It is an open problem whether Kirk's invariant is the complete obstruction to a link map being link homotopically trivial. With the objective of constructing counterexamples, Li proposed a link homotopy invariant that is defined on the kernel of and also obstructs link nullhomotopy. We …
Study shows how to create 2-links with any group in 4-manifolds.
problem Creating 2-links with any given group in 4-manifolds.
method Constructing simply connected 4-manifolds containing 2-links with specific properties.
result 2-links can have any group as their 2-link group.
The Hopf invariant is linked to null-homotopy properties of maps.
problem Understanding the relationship between the Hopf invariant and null-homotopy of maps.
method Using the generalized Hopf invariant and constructing smooth null-homotopies, the paper explores the relationship between the Hopf invariant and null-homotopy properties of maps.
result Sharp results on the relationship between the Hopf invariant and null-homotopy properties of maps, showing the necessity and sufficiency of certain conditions.
Abstract: Rational decomposition of homeomorphism spaces for manifolds.
problem Constructing rational homotopy pullback decompositions for homeomorphism spaces.
method Rational homotopy pullback decomposition, nullhomotopy of stabilisation maps, tensor products of truncated operads.
result Rational section of the stabilisation map for homeomorphisms of R^d.