what is the reaction of viewers when characters speak directly to the audience—breaking the invisible "fourth wall" of the theater—in films or television programs? Mel Brooks did this in "Blazing Saddles" and, more recently, Gary Shandling did in his television program with questions like: "Does my hair look OK?" This experiment using college students… (More)
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f (x) ∈ Z[x]. We establish the congruence p deg f k≡r (mod p α) n k (−1) k f k − r p α ≡ 0 mod p ∞ i=α n/p i (motivated by a conjecture arising from algebraic topology) and obtain the following vast generalization of Lucas' theorem: If α is greater than one, and l, s, t are… (More)
Hu and Kriz construct the real Johnson-Wilson spectrum, ER(n), which is 2 n+2 (2 n − 1)-periodic, from the 2(2 n − 1)-periodic spectrum E(n). ER(1) is just KO (2) and E(1) is just KU (2). We compute ER(n) * (RP ∞) and set up a Bock-stein spectral sequence to compute ER(n) * (−) from E(n) * (−). We combine these to compute ER(2) * (RP 2n) and use this to get… (More)
In this paper we compute the 3-primary v 1-periodic homotopy groups of the exceptional Lie group E 7. This represents the next stage in the author's goal of calculating the v 1-periodic homotopy groups of all compact simple Lie groups (at least when localized at an odd prime). Most of the work goes into calculating the unstable Novikov spectral sequence of… (More)
In this paper, we obtain the following new results regarding immersions and em-beddings of real projective space P m in Euclidean space. Let α(n) denote the number of 1's in the binary expansion of n.
This report presents a statistical profile of recipients of doctoral degrees awarded by departments in the mathematical sciences at universities in the United States during the period July 1, 2003, through June 30, 2004. It includes a preliminary analysis of the fall 2004 employment plans of 2003–04 doctoral recipients and a demographic profile summarizing… (More)
1. Statement of results Let p be a xed odd prime. The (p-local) v 1-periodic homotopy groups, v ?1 1 (X), of a space X were deened in 8]. Roughly speaking, they tell the portion of the p-local homotopy groups of X detected by K-theory. For a spherically resolved space X, each group v ?1 1 i (X) is a direct summand of some actual homotopy group L (X). We… (More)
The Dwyer–Wilkerson space DI(4) is the only exotic 2-compact group. We compute v −1 1 π * (DI(4)), its v1-periodic homotopy groups.