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 Jan12 comment Topological Meaning of semi-direct product Perhaps you could describe the topological meaning of the amalgamated free product you refer to first. This may help in garnering an analogous description for the semi-direct product. Jan11 comment Conceptual error in Kosinski's “Differential Manifolds”? As the textbook says on the bottom of pg 91 (at least in my 1993 edition), the existence of your g comes from Theorem 3.3.5 (pg 51) applied here with M={p}, N=M1, and F0, F1 your embeddings of Rm as tubular nbds of p. Then take g=H1 (as in the theorem statement). This has nothing to do with orientations. Jan6 answered Sphere with three Möbius strips glued and sphere with a handle and a Möbius strip glued Dec25 comment Proof of uniqueness of decomposition into prime knots Googling yields math.ucla.edu/~radko/191.1.05w/marcos.pdf for one proof. Dec19 comment How to apply Borel-Cantelli Lemma? To choose such a sequence $a_n$ requires $\mu$ (a probability measure on $[0,1]$?) to be absolutely continuous (Lebesgue measure of $A\subset [0,1] \Rightarrow \mu(A)=0$). Dec19 comment Doubts about Dominated Convergence Theorem @ Chris: judging from the first paragraph, I'd guess $T_h(x) = f(x-h)$. Dec18 revised Rephrasing a Convergence Result to make use of the Borel-Cantelli Lemma deleted 218 characters in body Dec18 answered Rephrasing a Convergence Result to make use of the Borel-Cantelli Lemma Dec15 awarded Scholar Dec15 awarded Supporter Dec15 accepted Homologous tori in 4-manifold Dec13 answered confusion about cup product in cohomology ring Dec13 awarded Teacher Dec13 answered Möbius transform example explanation Dec10 asked Homologous tori in 4-manifold Jun26 awarded Disciplined Jun24 awarded Editor Jun24 awarded Student