Braids and invariants of 3-manifolds.
Braids and Signatures
A braid defines a link which has a signature. This defines a map from the braid group to the integers which is not a homomorphism. We relate the homomorphism defect of this map to Meyer cocycle and Maslov class. We give some information about the global geometry of the gordian metric space.
Braids: generalizations, presentations and algorithmic properties.
Braids in Pau – An Introduction
In this work, we describe the historic links between the study of -dimensional manifolds (specially knot theory) and the study of the topology of complex plane curves with a particular attention to the role of braid groups and Alexander-like invariants (torsions, different instances of Alexander polynomials). We finish with detailed computations in an example.
Branched Coverings.
Branched coverings, triangulations, and 3-manifolds.
Branched covers according to J. W. Alexander.
Branched Covers of Surfaces in 4-Manifolds.
Branched Immersions of Surfaces and Reduction of Topological Type, I.
Branched Immersions of Surfaces and Reduction of Topological Type. II.
Branched ...-structures on surfaces with prescribed real holonomy.
Breaking Cycles on Surfaces.
Bridges and Hamiltonian circuits in planar graphs.
Brieskorn Complete Intersections and Automorphic Forms.
Brouwer degree, equivariant maps and tensor powers.
Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space
DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated...
Brown's representability theorem and branched coverings.
Brunnian links
A Brunnian link is a set of n linked loops such that every proper sublink is trivial. Simple Brunnian links have a natural algebraic representation. This is used to determine the form, length and number of minimal simple Brunnian links. Braids are used to investigate when two algebraic words represent equivalent simple Brunnian links that differ only in the arrangement of the component loops.
Brunnian links are determined by their complements.
Brunnian local moves of knots and Vassiliev invariants
K. Habiro gave a neccesary and sufficient condition for knots to have the same Vassiliev invariants in terms of -moves. In this paper we give another geometric condition in terms of Brunnian local moves. The proof is simple and self-contained.