Spectrum

Artist: Spectrum

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Formal Connection With:

King Harvest, Chants R&B

Genres: Rock
Representative Albums: "Ghosts (Post Terminal Reflection)

Biography

When latter-'60s psychedelic rock became the progressive rock of the early '70s, Melbourne's Spectrum was at the forefront of the Australian response. The group was formed from the ashes of Party Machine, which split up when singer and songwriter Ross Wilson left to join former Australian group Procession in London. Bass player Mike Rudd switched to lead guitar, and continued Party Machine's leaning toward lyrical satire.

EMI Australia added Spectrum to the company's global progressive Harvest label roster (Pink Floyd, Deep Purple etc.), and found amongst the group's experimental repertoire a melancholy, uncomplicated song called "I'll Be Gone," released as the group's first single. In May 1971, "I'll Be Gone" reached number one nationally, changing the group's fortunes dramatically. Prior to its release, Spectrum had struggled for gigs (promoters found them "too progressive") and the hot-shot young drummer Mark Kennedy, which was part of the band's live appeal, lost patience and left. Some observers thought the loss of the flashy and busily impressive drummer would be a blow and Spectrum wouldn't survive, but "I'll Be Gone" ensured the group's survival. Kennedy was replaced by the less explosive, more sympathetic Ray Arnott. Mike Rudd, in the meantime, refused to allow "I'll Be Gone" to be included on the album Spectrum Part One. It didn't fit with the innovative roaming style of the rest of the music on the album, more along the lines of progressive rock akin to post-Syd Barrett Pink Floyd and Traffic.

Spectrum's follow-up single "Trust Me" was an attempt to replicate their hit's commerciality, written and sung by the new drummer. But with the help of a second ambitious double album, Milesago, Spectrum had become one of Australia's first concert bands, preferring venues where they could use elaborate light shows. Step by step, Spectrum was becoming an event band. It became increasingly hard for them to present themselves at their optimum at the regular gigs, which were bread and butter for any working band in Australia in the '70s. To keep Spectrum's performances special, Mike Rudd invented an alter ego, Murtceps (Spectrum spelled backwards) with, apart from "I'll Be Gone," a repertoire all its own. Most important was the fact that the Indelible Murtceps was a stripped-back version of Spectrum, with no lightshows and a portable electric piano instead of the weighty Hammond organ allowing the band to play anywhere and often. Murtceps released its own singles and album.

The difficulty facing Spectrum's music and lineup defections caused Rudd and bass player Bill Putt to decide it would be simpler to put an end to Spectrum/Murtceps altogether. They started again with a new group, a new set of songs, and a new name, Ariel. Spectrum's final performance on April 15, 1973, was recorded as the double album Terminal Buzz.

The Rudd/Putt partnership endured through various bands and personal dilemmas until 1995 when they reinstated their Spectrum career with an independently released album, Living in a Volcano. They continue to perform under a variety of names but predominantly still call themselves Spectrum, although the most-recent version is more structured and song-oriented than the classic version of the group. Now "I'll Be Gone" fits perfectly.

"I'll Be Gone itself has become one of the classic Australian radio hits. There have been a number of cover versions. In 1974, Manfred Mann recorded a version for the rest of the world. ~ Ed Nimmervoll, All Music Guide

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Discography: Spectrum

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Milesago

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Ghosts (Post Terminal Reflection)

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Wikipedia: Spectrum (homotopy theory)

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In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. There are several different constructions of categories of spectra, all of which give the same homotopy category.

Suppose we start with a generalized cohomology theory E. This is a sequence of contravariant functors $E n$ from topological spaces to abelian groups, one for each integer n, which satisfy all of the Eilenberg-Steenrod axioms except for the dimension axiom. By the Brown representability theorem, $E n (X)$ is given by $[X, E n]$ , the set of homotopy classes of maps from X to $E n$ , for some space $E n$ . The isomorphism $E^n(X) \cong E^{n+1}(\Sigma X)$ , where $Σ X$ is the suspension of X, gives a map $\Sigma E_n \to E_{n+1}$ . This collection of spaces $E n$ together with connecting maps $\Sigma E_n \to E_{n+1}$ is a spectrum. In most (but not all) constructions of spectra the adjoint maps $E_n \to \Omega E_{n+1}$ are required to be weak equivalences or even homeomorphisms.

We can also construct homology and cohomology theories given a particular spectrum. We restrict attention to spectra whose spaces are pointed CW-complexes. Given a spectrum $E n$ , a subspectrum $F n$ is a sequence of subcomplexes that is also a spectrum. Noting that each i-cell in $E j$ becomes an (i+1)-cell in $E j + 1$ , a cofinal subspectrum is a subspectrum for which each cell of the parent spectrum is eventually contained in the subspectrum after a finite number of suspensions. Spectra can then be turned into a category by defining a map of spectra $f: E \to F$ to be a cofinal subspectrum $G$ of $E$ and a sequence of pointed maps $f_n: G_n \to F_n$ such that $Sf_n = f_{n+1|G_n}$ (i.e. the obvious square commutes). Intuitively such a map of spectra does not need to be everywhere defined, just eventually become defined, and two maps that coincide on a cofinal subspectrum are said to be equivalent. The smash product of a spectrum $E$ and a pointed complex $X$ is a spectrum given by $(E \wedge X)_n = E_n \wedge X$ (associativity of the smash product yields immediately that this is indeed a spectrum). A homotopy of spectra corresponds to a map $(E \wedge I^+) \to F$ , where $I +$ is the disjoint union $[0, 1] \sqcup \{*\}$ with * taken to be the basepoint. Finally, we can define the suspension of a spectrum as $(Σ E) n = E n + 1$ .

Given all this information, we can first note that there is an inverse to the suspension functor given by $(Σ - 1 E) n + 1 = E n$ . We can define the homotopy groups of a spectrum to be those given by $π n E = [Σ n S, E]$ , where $S$ is the spectrum of spheres and $[X, Y]$ is the set of homotopy classes of maps from $X$ to $Y$ . Using some facts about what are commonly called "cofiber sequences of spectra" we arrive at the definitions $E_n X = \pi_n (E \wedge X) = [\Sigma^n S, E \wedge X]$ and $E^n X = [\Sigma^{-n} S \wedge X, E]$ for the homology and cohomology theories respectively associated to the spectrum $E$ . It is worth noting that $S_n X = \pi_n(S \wedge X)$ corresponds to the nth stable homotopy group of $X$ .

Examples

Consider singular cohomology $H n (X; A)$ with coefficients in an abelian group A. By Brown representability $H n (X; A)$ is the set of homotopy classes of maps from X to K(A,n), the Eilenberg-MacLane space with homotopy concentrated in degree n. Then the corresponding spectrum HA has n'th space K(A,n); it is called the Eilenberg-MacLane spectrum.

As a second important example, consider topological K-theory. At least for X compact, $K 0 (X)$ is defined to be the Grothendieck group of the monoid of complex vector bundles on X. Also, $K 1 (X)$ is the group corresponding to vector bundles on the suspension of X. Topological K-theory is a generalized cohomology theory, so it gives a spectrum. The zero'th space is $\mathbf{Z} \times BU$ while the first space is $U$ . Here $U$ is the infinite unitary group and $B U$ is its classifying space. By Bott periodicity we get $K^{2n}(X) \cong K^0(X)$ and $K^{2n+1}(X) \cong K^1(X)$ for all n, so all the spaces in the topological K-theory spectrum are given by either $\mathbf{Z} \times BU$ or $U$ . There is a corresponding construction using real vector bundles instead of complex vector bundles, which gives an 8-periodic spectrum.

For many more examples, see the list of cohomology theories.

History

A version of the concept of a spectrum was introduced in the 1958 doctoral dissertation of Elon Lages Lima. His advisor Edwin Spanier wrote further on the subject in 1959. There was development of the topic by J. Michael Boardman, amongst others. The above setting came together during the mid-1960s, and is still used for many purposes: see Adams (1974) or Vogt (1970). Important further theoretical advances have however been made since 1990, improving vastly the formal properties of spectra. Consequently, much recent literature uses modified (and highly technical) definitions of spectrum: see Mandell et al. (2001) for a unified treatment of these new approaches.

References

J. F. Adams (1974). "Stable homotopy and generalised homology". University of Chicago Press.

Mandell, M. A.; May,, J. P.; Schwede, S.; Shipley, B. (2001), "Model categories of diagram spectra", Proc. London Math. Soc. (3) 82: 441–512, doi:10.1112/S0024611501012692

R. Vogt (1970). "Boardman's stable homotopy category". Lecture note series No. 21, Matematisk Institut, Aarhus University.

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		Artist. Copyright © 2009 All Media Guide, LLC. Content provided by All Music Guide ®, a trademark of All Media Guide, LLC. All rights reserved. Read more
		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Spectrum (homotopy theory)". Read more

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