Timeline for More questions about Verdier duality (and related math)

5 events

when toggle format	what		by	license	comment
Dec 28, 2019 at 22:55	comment	added	Greg Friedman		Sorry, I should have said more explicitly something like "singular chain cap product." Iversen does have a Poincare duality theorem with isomorphism given by a map he calls a cap product, but that map is defined in his book purely sheaf theoretically. So it's not obvious, at least not to me, that this is the same Poincare duality isomorphism you can find proven in a more classical algebraic topology text (e.g. Hatcher, Spanier, Munkres, Dold, etc.).
Dec 27, 2019 at 18:23	comment	added	user20948		Sorry, I don't understand why you stressed that the comparison to classical Poincaré duality is "far from obvious" (that is to say, the others are "more obvious")? It is Theorem 4.7 in Iversen's Cohomology of Sheaves. I am struggling to establish a proof on my own, but I don't see how this one should be especially more difficult than others.
Jun 27, 2011 at 6:12	comment	added	Greg Friedman		I mean the n-k cohomology group of $M$ with coefficients in the orientation sheaf $\omega$. More explicitly, this would be $H^{n-k}(\Gamma(M;I^\ast))$, where $I^\ast$ is an injective resolution of $\omega$. Or it could be the Cech cohomology with coefficients in $\omega$ if you like that better.
Jun 24, 2011 at 12:47	comment	added	James D. Taylor		What do you mean by $H^{n-k}(M,\omega)$?
Jun 24, 2011 at 5:12	history	answered	Greg Friedman	CC BY-SA 3.0