Poincare submersions

We prove two kinds of fibering theorems for maps X --> P, where X and P are Poincare spaces. The special case of P = S^1 yields a Poincare duality analogue of the fibering theorem of Browder and Levine.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-2.abs.html Version 5: Statement of Theorem B corrected, see footnote p2

String Area Chamber & Solo Recital

String Area Chamber & Solo RecitalMonday, April 15, 2019 at 1:30pmRecital Hall / James W. Black Music Center1015 Grove Avenue / Richmond, Va

In Defense of Wishful Thinking: James, Quine, Emotions, and the Web of Belief

What is W. V. O. Quine’s relationship to classical pragmatism? Although he resists the comparison to William James in particular, commentators have seen an affinity between his “web of belief” model of theory confirmation and James’s claim that our beliefs form a “stock” that faces new experience as a corporate body. I argue that the similarity is only superficial. James thinks our web of beliefs should be responsive not just to perceptual but also to emotional experiences in some cases; Quine denies this. I motivate James’s controversial view by appealing to an episode in the history of medicine when a researcher self-experimented by swallowing a vial of bacteria that at the time had not been studied in much detail. The researcher’s commitment to his own as-yet untested hypothesis was based in part on emotional considerations. Finally, I argue that Quine’s insistence that emotions can never be relevant to adjusting our web of belief reflects a tacit holdover of one of logical positivism’s crucially anti-pragmatist commitments—that philosophy of science should focus exclusively on the context of justification, not the context of discovery. James’s emphasis on discovery as a (perhaps the) crucial locus for epistemological inquiry is characteristic of pragmatism in general. Since Quinean epistemology is always an epistemology of justification, he is not happily viewed as a member of the pragmatist tradition

Muon Production in Relativistic Cosmic-Ray Interactions

Cosmic-rays with energies up to $3\times10^{20}$ eV have been observed. The nuclear composition of these cosmic rays is unknown but if the incident nuclei are protons then the corresponding center of mass energy is $\sqrt{s_{nn}} = 700$ TeV. High energy muons can be used to probe the composition of these incident nuclei. The energy spectra of high-energy ($>$ 1 TeV) cosmic ray induced muons have been measured with deep underground or under-ice detectors. These muons come from pion and kaon decays and from charm production in the atmosphere. Terrestrial experiments are most sensitive to far-forward muons so the production rates are sensitive to high-$x$ partons in the incident nucleus and low-$x$ partons in the nitrogen/oxygen targets. Muon measurements can complement the central-particle data collected at colliders. This paper will review muon production data and discuss some non-perturbative (soft) models that have been used to interpret the data. I will show measurements of TeV muon transverse momentum ($p_T$) spectra in cosmic-ray air showers from MACRO, and describe how the IceCube neutrino observatory and the proposed Km3Net detector will extend these measurements to a higher $p_T$ region where perturbative QCD should apply. With a 1 km$^2$ surface area, the full IceCube detector should observe hundreds of muons/year with $p_T$ in the pQCD regime.Comment: 4 pages, 2 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee. Tweaked formatting at organizers reques

Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space. I

Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact treatment (``solvable'' and/or ``integrable'' and/or ``linearizable''). These equations of motion are always rotation-invariant, and sometimes translation-invariant as well. In many cases they are Hamiltonian, but the discussion of this aspect is postponed to a subsequent paper. We consider ``few-body problems'' (with, say, \textit{N}=1,2,3,4,6,8,12,16,...) as well as ``many-body problems'' (N an arbitrary positive integer). The main focus of this paper is on various techniques to uncover such N-body problems. We do not discuss the detailed behavior of the solutions of all these problems, but we do identify several models whose motions are completely periodic or multiply periodic, and we exhibit in rather explicit form the solutions in some cases

The Dualizing Spectrum, II

To an inclusion topological groups H->G, we associate a naive G-spectrum. The special case when H=G gives the dualizing spectrum D_G introduced by the author in the first paper of this series. The main application will be to give a purely homotopy theoretic construction of Poincare embeddings in stable codimension.Comment: Fixed an array of typo