Spaces of embeddings of compact polyhedra into 2-manifolds

Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E(X, M) denote the space of embeddings of X into M with the compact-open topology. In this paper we study an extension property of embeddings of X into M and show that the restriction map from the homeomorphism group of M to E(X, M) is a principal bundle. As an application we show that if M is a Euclidean PL 2-manifold and dim X >= 1 then the triple (E(X,M), E^LIP(X,M), E^PL(X, M)) is an (s,Sigma,sigma)-manifold, where E_K^LIP(X,M) and E_K^PL(X, M) denote the subspaces of Lipschitz and PL embeddings.Comment: 13 page

A quantitative version of the commutator theorem for zero trace matrices

Let $A$ be a $m\times m$ complex matrix with zero trace and let \e>0. Then there are $m\times m$ matrices $B$ and $C$ such that $A=[B,C]$ and \|B\|\|C\|\le K_\e m^\e\|A\| where K_\e depends only on \e. Moreover, the matrix $B$ can be taken to be normal

Triangle-roundedness in matroids

A matroid $N$ is said to be triangle-rounded in a class of matroids $\mathcal{M}$ if each $3$-connected matroid $M\in \mathcal{M}$ with a triangle $T$ and an $N$-minor has an $N$-minor with $T$ as triangle. Reid gave a result useful to identify such matroids as stated next: suppose that $M$ is a binary $3$-connected matroid with a $3$-connected minor $N$, $T$ is a triangle of $M$ and $e\in T\cap E(N)$; then $M$ has a $3$-connected minor $M'$ with an $N$-minor such that $T$ is a triangle of $M'$ and $|E(M')|\le |E(N)|+2$. We strengthen this result by dropping the condition that such element $e$ exists and proving that there is a $3$-connected minor $M'$ of $M$ with an $N$-minor $N'$ such that $T$ is a triangle of $M'$ and $E(M')-E(N')\subseteq T$. This result is extended to the non-binary case and, as an application, we prove that $M(K_5)$ is triangle-rounded in the class of the regular matroids

Wellcome Witnesses to Twentieth Century Medicine: Volume 2

Annotated and edited transcripts of 4 Witness Seminars. Introduction by E M Tansey. First published by the Wellcome Trust, 1998 Occasional Publication no. 6, 1998. ©The Trustee of the Wellcome Trust, London, 1998.All volumes are freely available online following the links to Publications/Wellcome Witnesses at www.ucl.ac.uk/histmed.Annotated and edited transcripts of 4 Witness Seminars. Introduction by E M Tansey.Annotated and edited transcripts of 4 Witness Seminars. Introduction by E M Tansey.Annotated and edited transcripts of 4 Witness Seminars. Introduction by E M Tansey.Annotated and edited transcripts of 4 Witness Seminars. Introduction by E M Tansey.Annotated and edited transcripts of 4 Witness Seminars. Introduction by E M Tansey.Annotated and edited transcripts of 4 Witness Seminars. Introduction by E M Tansey.Second volume of four Witness Seminar transcripts of meetings held between 1996 and 1997: ‘Making the Human Body Transparent: The Impact of Nuclear Magnetic Resonance and Magnetic Resonance Imaging’ (Tansey E M, Christie D A, eds); ‘Research in General Practice’ (Tansey E M, Reynolds L A, eds); ‘Drugs in Psychiatric Practice’ (Tansey E M, Christie D A, eds); ‘The MRC Common Cold Unit (Tansey E M, Reynolds L A, eds). Tansey E M, Christie D A, Reynolds L A. (eds) (1998) Wellcome Witnesses to Twentieth Century Medicine: Volume 2. London: The Wellcome Trust.The Wellcome Trust is a registered charity, no. 210183