# Grumpy Parsnip

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bio website math.utk.edu/~jconant location Knoxville, TN age 38 member for 2 years, 6 months seen 26 mins ago profile views 1,868

I like low-dimensional topology and geometric group theory. I'm particularly drawn to problems that involve algebraic spaces of graphs, such as graph homology.

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 May7 revised Induced map on homology from a covering space isomorphismadded 1380 characters in body May7 revised Induced map on homology from a covering space isomorphismedited body May7 revised Induced map on homology from a covering space isomorphismadded 290 characters in body May7 revised Induced map on homology from a covering space isomorphismadded 290 characters in body May7 answered Induced map on homology from a covering space isomorphism May7 comment Question on Good PairsYou are on the right track in both cases. May7 comment Help with an inequality problem@chubakueno: no, because you could have several minima, or none at all. All you know is that the set of minima must be symmetric. May7 comment Help with an inequality problemIf you somehow know that there is a unique answer, then because the equations are symmetric with respect to $a,b,c$, all coordinates must be equal. May7 comment Length of DNA strandThe community tends to prefer questions that are actually questions and not posed in the imperative. May6 comment Classifying Vector Bundles@rondo9: Unless you allow a space to be a $0$-dimensional bundle over itself, then no. Every vector bundle is not compact for example. May6 answered Classifying Vector Bundles May6 comment Is $f$ necessarily a covering?You are right. That's a good point. May6 awarded Caucus May6 comment Is $f$ necessarily a covering?I don't see anywhere where the locally path connected property was used though. May6 comment Is $f$ necessarily a covering?Indeed, let $f^{-1}(y)=\{x_1,\ldots,x_n\}$ and let $U_{x_i}$ be an open set in $X$ containing $x_i$ as stated in the problem. Let $W=\cap_{i=1}^n f(U_{x_i})$. Then $W$ is an evenly covered neighborhood of $Y$. May6 comment to find disconnected graphs@monalisa: this is called the Euler characteristic. The loops I am referring to are not the same as what you are thinking, though. For me a loop is a "hole" in the graph, and as I mentioned in my comment, this can be rigorously defined as the number of edges in the complement of a spanning forest. May6 comment How to find the limit of $\dfrac{\ln(\ln(\frac{n}{n-1}))}{\ln(n)}$?There's a minus sign missing in your last inequality. May6 comment to find disconnected graphsThere's a nice formula that is often useful: $V-E=b_0-b_1$ where $V,E$ are the number of vertices and edges, $b_0$ is the number of connected components and $b_1$ is the "number of loops," which can be defined as the number of edges in the complement of a spanning forest. May5 answered Hatcher 2.2 Exercise 33 May5 comment If two Lie Groups are homomorphic, does that mean that they are homeomorphic?@BabyDragon: yes. Both are vector spaces over $\mathbb Q$ of the same uncountable dimension.