Grumpy Parsnip

9,584 reputation

11347

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

	9,584 reputation	bio	website	math.utk.edu/~jconant	visits	member for	2 years, 6 months
11347 badges		location	Knoxville, TN		seen	26 mins ago

summary answers questions tags badges favorites bounties reputation activity

1,230 Actions

suggestions reviews revisions comments badges posts accepts all

May 7	revised	Induced map on homology from a covering space isomorphism added 1380 characters in body
May 7	revised	Induced map on homology from a covering space isomorphism edited body
May 7	revised	Induced map on homology from a covering space isomorphism added 290 characters in body
May 7	revised	Induced map on homology from a covering space isomorphism added 290 characters in body
May 7	answered	Induced map on homology from a covering space isomorphism
May 7	comment	Question on Good Pairs You are on the right track in both cases.
May 7	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.
May 7	comment	Help with an inequality problem If 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.
May 7	comment	Length of DNA strand The community tends to prefer questions that are actually questions and not posed in the imperative.
May 6	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.
May 6	answered	Classifying Vector Bundles
May 6	comment	Is $f$ necessarily a covering? You are right. That's a good point.
May 6	awarded	Caucus
May 6	comment	Is $f$ necessarily a covering? I don't see anywhere where the locally path connected property was used though.
May 6	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 $Y$.
May 6	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.
May 6	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.
May 6	comment	to find disconnected graphs There'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.
May 5	answered	Hatcher 2.2 Exercise 33
May 5	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.