Results 1  10
of
70
Homotopical Patch Theory
"... Homotopy type theory is an extension of MartinLöf type theory, based on a correspondence with homotopy theory and higher category theory. In homotopy type theory, the propositional equality type becomes proofrelevant, and corresponds to paths in a space. This allows for a new class of datatypes, ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
, called higher inductive types, which are specified by constructors not only for points but also for paths. In this paper, we consider a programming application of higher inductive types. Version control systems such as Darcs are based on the notion of patches—syntactic representations of edits to a
Computing Homotopic Shortest Paths Efficiently
"... Abstract. We give algorithms to find shortest paths homotopic to givendisjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k log n+npn), and the randomized version in time O(k log n+ n(log n)1+"), where k is the input plus outputsizes o ..."
Abstract
 Add to MetaCart
Abstract. We give algorithms to find shortest paths homotopic to givendisjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(k log n+npn), and the randomized version in time O(k log n+ n(log n)1+"), where k is the input plus outputsizes
HOMOTOPICALLY PERIODIC MAPS OF MODEL ASPHERICAL MANIFOLDS
"... For a closed orientable surface S, anymap f: S → S whose nth power is homotopic to the identity, is homotopic to a homeomorphism g of S of order n. This famous theorem of Nielsen is known to fail in general for aspherical manifolds. In this paper, for model aspherical manifolds M associated to a fi ..."
Abstract
 Add to MetaCart
finitelyextendable set of data, we, however, present a weaker version of Nielsen’s result. We show that anyhomotopically periodic selfmap f of M is homotopic to a fiber preserving homeomorphism g of M of finite order (but the order of g is not necessarilyequal to the homotopyperiod of f). 1. Introduction
HOMOTOPICAL EQUIVALENCE OF COMBINATORIAL AND CATEGORICAL SEMANTICS OF PROCESS ALGEBRA
, 711
"... Abstract. It is possible to translate a modified version of K. Worytkiewicz’s combinatorial semantics of CCS (Milner’s Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled flows using a geometric realization functor. It turn ..."
Abstract
 Add to MetaCart
Abstract. It is possible to translate a modified version of K. Worytkiewicz’s combinatorial semantics of CCS (Milner’s Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled flows using a geometric realization functor
© Hindawi Publishing Corp. MINIMIZING ENERGY AMONG HOMOTOPIC MAPS
, 2003
"... We study an energy minimizing sequence {ui} in a fixed homotopy class of smooth maps from a 3manifold. After deriving an approximate monotonicity property for {ui} and a continuous version of the Luckhaus lemma (Simon, 1996) on S2, we show that, passing to a subsequence, {ui} converges strongly in ..."
Abstract
 Add to MetaCart
We study an energy minimizing sequence {ui} in a fixed homotopy class of smooth maps from a 3manifold. After deriving an approximate monotonicity property for {ui} and a continuous version of the Luckhaus lemma (Simon, 1996) on S2, we show that, passing to a subsequence, {ui} converges strongly
Topological equivalences for differential graded algebras
 Adv. Math
, 2006
"... Abstract. We investigate the relationship between differential graded algebras (dgas) and topological ring spectra. Every dga C gives rise to an EilenbergMac Lane ring spectrum denoted HC. If HC and HD are weakly equivalent, then we say C and D are topologically equivalent. Quasiisomorphic dgas are ..."
Abstract

Cited by 20 (7 self)
 Add to MetaCart
are topologically equivalent, but we produce explicit counterexamples of the converse. We also develop an associated notion of topological Morita equivalence using a homotopical version of tilting. Contents
Volume gradients and homology in towers of residually free groups
 Preprint, 2013, arXiv:1309.1877. 1062 RANK AND DEFICIENCY GRADIENTS OF THOMPSON GROUPS
"... Abstract. We study the asymptotic growth of homology groups and the cellular volume of classifying spaces as one passes to normal subgroups Gn < G of increasing finite index in a fixed finitely generated group G, assuming n Gn = 1. We focus in particular on finitely presented residually free gro ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
groups, calculating their 2 betti numbers, rank gradient and asymptotic deficiency. If G is a limit group and K is any field, then for all j ≥ 1 the limit of dim H j (Gn, K)/[G, Gn] as n → ∞ exists and is zero except for j = 1, where it equals −χ(G). We prove a homotopical version of this theorem
The equivariant ConnerFloyd isomorphism
 Trans. Amer. Math. Soc
"... ABSTRACT. This paper proves two equivariant generalizations of the ConnerFloyd isomorphism relating unitary cobordism and Ktheory. It extends a previous result of Okonek for abelian groups to all compact Lie groups. We also show that the result for finite groups is true using either the geometric ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
or homotopical versions of cobordism. 1. Introduction. In [6] Conner and Floyd established a relation between cobordism and.rftheory. They proved that MU*(X)®MU.K * = k*(X), where MU is unitary cobordism and K is complex Ä"theory. A generalization of this result to the equivariant context was proved
FOLIATIONS WITH ONE–SIDED BRANCHING VERSION 0.7
, 2001
"... Abstract. We generalize the main results from [19] and [2] to taut foliations with one–sided branching. First constructed by Meigniez in [13], these foliations occupy an intermediate position between R–covered and arbitrary taut foliations of 3–manifolds. We show that for a taut foliation F with one ..."
Abstract
 Add to MetaCart
of the universal cover, and co–orient ˜ F so that the leaf space branches in the negative direction. Then for any pair of leaves of ˜ F with µ> λ, the leaf λ is asymptotic to µ in a dense set of directions at infinity. This is a macroscopic version of an infinitesimal result in [20] and gives much more drastic
Results 1  10
of
70