A genus for N-dimensional knots and links.
A geometric decomposition of spaces into cells of different types.
A graph-theoretical representation of PL-manifolds - A survey on crystallizations.
A necessary condition for embedding a complex in
A new invariant and parametric connected sum of embeddings
We define an isotopy invariant of embeddings of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected...
A non-𝒵-compactifiable polyhedron whose product with the Hilbert cube is 𝒵-compactifiable
We construct a locally compact 2-dimensional polyhedron X which does not admit a 𝒵-compactification, but which becomes 𝒵-compactifiable upon crossing with the Hilbert cube. This answers a long-standing question posed by Chapman and Siebenmann in 1976 and repeated in the 1976, 1979 and 1990 versions of Open Problems in Infinite-Dimensional Topology. Our solution corrects an error in the 1990 problem list.
A Note on Higher Dimensional Knots.
A Quick proof of Singhof's cat (M x S1) = cat (M) + 1 theorem.
A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion
We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a -regular or -representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a -bridge knot and -representations of its knot group.
A Semigroup of Simple Homotopy Types.
A short proof of the uniqueness of Kühnel's 9-vertex complex projective plane.
A simpler construction of volume polynomials for a polyhedron.
A Splitting Theorem for Manifolds.
A theorem of Sanderson on link bordisms in dimension 4.
A topological collapse number for all spaces
A topological resolution theorem
A Total Whitehead Torsion Obstruction to Fibering over the Circle.
A uniform approach to complexes arising from forests.
A user's guide to discrete Morse theory.
A Vanishing Theorem for Euler Characteristics.