MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

# Lee Mosher

 6,109 Reputation 2144 views

## Registered User

 Name Lee Mosher Member for 1 year Seen 6 hours ago Website Location Rutgers University, Newark Age
 8h comment embeddings of graphs into surfacesRegarding question 1, your two assumptions together imply that $rank(\Gamma)=2genus(S)$, because the first says $1−r \ge 1−2g$ and surjectivity of $i_∗$ implies $r \ge 2g$. Is that the intent? 2d comment Why is the length R cosine theta?Your question, while interesting, is off topic at this site, which is for questions of mathematical research. Try another site like math.stackexchange.com Jun15 accepted What are the best settings for the large scale geometry of locally compact groups? Jun15 answered Why are negative sets multisets? (Reference request) Jun14 comment What is the moduli space of germs of one-sided complex structures near the circle?My answer is written with sufficient generality to cover that assumption: the cusp is ruled out, and only the other case remains. Jun14 answered What is the moduli space of germs of one-sided complex structures near the circle? Jun13 comment Proper Group action on a metric spaceBeing a length metric is irrelevant. On the other hand, you ought to assume the metric space is proper (closed balls are compact), particularly since you are assuming that the action is proper (the induced map $G \times X \to X \times X$ is a proper function). In that case what you ask for is true, and is a trivial consequence of the definitions. Jun13 comment What are the best settings for the large scale geometry of locally compact groups?And I see that my answer has crossed with David's pointer to Yves Cornulier's paper. Jun13 answered What are the best settings for the large scale geometry of locally compact groups? Jun12 answered Random metrics on compact orientable surfaces Jun12 comment Distortion of tree embedding in Alexandrov spacesOops, sorry, my eyes saw "non-negative" and my brain saw "non-positive". Jun12 comment Distortion of tree embedding in Alexandrov spacesYou might want a narrower focus which rules out negatively curved spaces in which the infinite binary tree embeds with uniform value of $D$. Jun3 comment Where to look for corrections of papers?If the paper is published in a journal and has a published correction, sometimes MathSciNet will bundle the review of the original paper and its correction into a single entry; the extreme rarity of this practice is a clue to the extreme rarity of published corrections. Also, if you have downloaded the paper from the arXiv, keep a lookout for later versions on the arXiv or in a journal, either of which is quite likely to contain corrections/revisions/updates of earlier versions. May31 comment Geometry defined by foliation.Do you mean "lines PARALLEL to each axis"? May29 comment Is there any finitely-long sequence of digits which is not found in the digits of pi?Voting to close meta.mathoverflow.net/discussion/1601/… May28 comment complete metric spaceWhat is left unsaid in the answer and the wikipedia link is that the original metric and the "intrinsic metric" can be pathologically different. For example, if $X$ is the Cantor set or any other totally disconnected metric space then dist completely degenerates to the unique $0,\infty$ extended metric. May26 comment Universal covering of compact surfacesDaniele's construction is not so much an application of the classification of surfaces, and more an application of the Poincare polygon theorem, in order to obtain the universal covering map with domain $\mathbb{H}^2$ using the gluing pattern for the specific surface asked for by the OP. May25 revised Classification of geometric outer automorphisms of free groupsadded 529 characters in body May25 answered Universal covering of compact surfaces May23 comment $P^1$ minus k pointsThe derivation of the matrices should be covered in any textbook on hyperbolic geometry. In outline, if you fix the polygon $P$ in the upper half plane model, each side pairing $a_i \mapsto \bar a_i$ takes the endpoints of $a_i$ to the endpoints of $\bar a_i$. Once the image of a third point at infinity is determined, the matrix is determined. There is also a completeness condition for each cusp: the monodromy around that cusp must be parabolic. With that, you get a very explicit set of formulas parameterizing the matrices. May23 revised Hyperbolic pair of pants.added 74 characters in body May23 revised Hyperbolic pair of pants.deleted 102 characters in body; edited body May23 revised Hyperbolic pair of pants.deleted 14 characters in body May23 answered Hyperbolic pair of pants. May22 answered $P^1$ minus k points May22 comment Does this qualify as “self plagiarism” or something?Here is a general rule which I tell my students when they need to write background material which they learned from another source, and which perhaps applies to material from ones own earlier writings. Don't be lazy: learn the old references in your heart of hearts, and then rewrite it anew the way you need it for your current paper. May21 comment What does a singular simplex with real coefficient mean Perhaps you meant "references on singular homology". I would recommend Hatcher's book, which explains the distinctions between simplicial homology and singular homology. It is available at math.cornell.edu/~hatcher/AT/ATpage.html May20 comment What does “Vertex Solution” mean?A citation of the paper or book in which you found this phrase, for example. May18 comment What is an interpretation of the relation in the cohomology of the pure braid groups?At least you will have a lot of time to draw pictures of braids in the sand. May16 revised Computation of Ext(Z^N,Z)edited body May16 comment What are these compact sets called?How about just a "piecewise smooth set"? May13 comment Mapping class group of once-punctured torusI guess what I mean is that what I would write in this situation is: "The proof for $T$ is given in [FLP], and the proof for $S$ follows immediately from the definitions." May13 answered The role of the Automatic Groups in the history of Geometric Group Theory May13 answered Mapping class group of once-punctured torus May9 comment Jordan curve theorem: Can every point on the curve be reached from each region? Actually, what you state is not the full "Jordan Schonflies theorem". The full statement of the Schonflies theorem is that there is a homeomorphism of the plane taking $C$ to $S^1$, from which your property follows easily. May9 revised Trees in groups of exponential growthedited tags May9 accepted Converse to Milnor’s theorem on manifolds with nonnegative Ricci curvature. May9 revised Converse to Milnor’s theorem on manifolds with nonnegative Ricci curvature. added tag geometric-group-theory May8 revised Converse to Milnor’s theorem on manifolds with nonnegative Ricci curvature. added 81 characters in body May8 revised Converse to Milnor’s theorem on manifolds with nonnegative Ricci curvature. added 89 characters in body May8 answered Converse to Milnor’s theorem on manifolds with nonnegative Ricci curvature. May8 comment Discrete disjoint covering of integer lattices@Some guy: This change, from "basis-and-origin simplex" to "minimal integer simplex", changes the mathematical content of your question and confuses the issue. For example, {(0,0),(34,21),(21,13)} is a "minimal integer" simplex, but it is not a translate of the basis-and-origin simplex. Was that your intent? May7 revised Dehn presentation of a knot groupedited tags May7 revised Why isn’t $\langle x,y,z|xyzx^{-1}y^{-1}z^{-1}\rangle$ a hyperbolic surface group?edited tags; edited tags May7 revised Polynomial growth of the Betti number of balls of the Cayley graphsedited tags May7 comment Periodic automorphisms of free groups and surface homeomorphismsYou're welcome, Sebastian. May7 accepted Periodic automorphisms of free groups and surface homeomorphisms May6 answered Classification of geometric outer automorphisms of free groups May6 answered Periodic automorphisms of free groups and surface homeomorphisms May6 comment Periodic automorphisms of free groups and surface homeomorphismsWhen you speak about automorphisms of free groups, do you really mean outer automorphisms? I ask because $h : M \to M$ does not induce a well-defined automorphism of $\pi_1 M$, at best it induces an outer automorphism.