2 6 N ov 2 00 4 An alternative approach to homotopy operations

1 6 N ov 2 00 5 The pre - WDVV ring of physics and its topology ∗

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-VerlindeVerlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex ∆n is homotopy equivalent to a wedge of (n − 2)! spheres of dimension n − 4. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the fa...

2 5 N ov 2 00 4 WITT VECTORS AND EQUIVARIANT RING SPECTRA

This paper establishes a connection between equivariant ring spectra and Witt vectors in the sense of Dress and Siebeneicher. Given a commutative ringspectrum T in the highly structured sense, that is, an E∞-ringspectrum, with action of a finite group G we construct a ringhomomorphism from the ring of G-typical Witt vectors of the zeroth homotopy group of T to the zeroth homotopy group of the G...

N ov 2 00 8 EQUIVARIANT CW - COMPLEXES AND THE ORBIT CATEGORY

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S 5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.

. A T ] 7 S ep 2 00 5 A NUMBER - THEORETIC APPROACH TO HOMOTOPY EXPONENTS OF SU ( n ) DONALD

Let p be a prime number. The homotopy p-exponent of a topological space X, denoted by expp(X), is defined to be the largest e ∈ N = {0, 1, 2, . . .} such that some homotopy group πi(X) has an element of order p . This concept has been studied by various topologists (cf. [3], [4], [12], [15], [16], and [5]). The most celebrated result about homotopy exponents (proved by Cohen, Moore, and Neisend...

N ov 2 00 6 Measurements of K e 4 and K ± → π 0 π 0 π ± decays