154 research outputs found
Properties of three functions relating to the exponential function and the existence of partitions of unity
In the paper, the author studies properties of three functions relating to
the exponential function and the existence of partitions of unity, including
accurate and explicit computation of their derivatives, analyticity, complete
monotonicity, logarithmically complete monotonicity, absolute monotonicity, and
the like.Comment: 5 page
A characterization of submanifolds by a homogeneity condition
A very short proof of the following smooth homogeneity theorem of D. Repovs,
E. V. Scepin and the author is presented.
Let N be a locally compact subset of a smooth manifold M. Assume that for
each two points x,y in N there exist their neighborhoods Ux and Uy in M and a
diffeomorphism h : Ux \to Uy such that h(x)=y and h (Ux \cap N) = Uy \cap N.
Then N is a smooth submanifold of M.Comment: 4 pages, meaning-distorting typos correcte
Cork twisting Schoenflies problem
The stable Andrews-Curtis conjecture in combinatorial group theory is the
statement that every balanced presentation of the trivial group can be
simplified to the trivial form by elementary moves corresponding to
"handle-slides" together with "stabilization" moves. Schoenflies conjecture is
the statement that the complement of any smooth embedding S^3 into S^4 are pair
of smooth balls. Here we suggest an approach to these problems by certain cork
twisting operation on contractible manifolds, and demonstrate it on the example
of the first Cappell-Shaneson homotopy sphere.Comment: 10 pages, 17 figure
The existence of thick triangulations -- an "elementary" proof
We provide an alternative, simpler proof of the existence of thick
triangulations for noncompact manifolds. Moreover, this proof
is simpler than the original one given in \cite{pe}, since it mainly uses tools
of elementary differential topology. The role played by curvatures in this
construction is also emphasized.Comment: 7 pages Short not
- …