Poincaré Duality is closely related to the Thom Isomorphism Theorem, as we will explain here.

:* the Thom Isomorphism.

This map is well-defined as there is a standard identification which is an oriented bundle, so the Thom Isomorphism applies.

This formulation of Poincaré Duality has become quite popular as it provides a means to define Poincaré Duality for any generalized homology theories provided one has a Thom Isomorphism for that homology theory.

More specifically, there is a general Poincaré duality theorem for generalized homology theories which requires a notion of orientation with respect to a homology theory, and is formulated in terms of a generalized Thom Isomorphism Theorem.

The books begin in the Year of the Fall 1103, when the protagonist Raj Whitehall and his friend Thom Poplanich stumble on a still-working remnant of the old technology, the quantum supercomputer " Center ", which Raj and Thom regard as an angel.

" Thom Jurek from Allmusic wrote: " part of an emotional journey as complete as can be.

The Hanging Garden is a 1997 British / Canadian movie written and directed by Thom Fitzgerald that is about the duality of life and death and the way seemingly very different choices in life can lead to similar outcomes.

Catastrophe theory, which originated with the work of the French mathematician René Thom in the 1960s, and became very popular due to the efforts of Christopher Zeeman in the 1970s, considers the special case where the long-run stable equilibrium can be identified with the minimum of a smooth, well-defined potential function ( Lyapunov function ).

The temple can be seen on the left side when entering Angkor Thom at the southern gate.

Another view is that the Nebra disk can be linked to the solar calendar reconstructed by Alexander Thom from his analysis of standing stone alignments in Britain.

Complex bordism is a generalized homology theory, corresponding to a spectrum MU that can be described explicitly in terms of Thom spaces as follows.

We can loosely interpret the theorem as being a generalization of the suspension isomorphism on ( co ) homology, because the Thom space of a trivial bundle on B of rank k is isomorphic to the kth suspension of B +, B with a disjoint point added.

Denote this Thom class by U. Then for a class b in the cohomology of the base, we can compute the Thom isomorphism via the pullback of the bundle projection and the cohomology cup product:

Thom, on the other hand, is a proponent of the circle builders being adept astronomers and mathematicians and suggests that these skills can be seen in all stone circles, everywhere.

Thom applied the statistical lumped variance test of J. R. Broadbent on this quantum and found the results significant while others have challenged his statistical analysis and suggested that Thom's evidence can be explained in other ways, for instance the average length of a pace.

Examples of this diversity can seen through its street theatre programme, directed by Thom McGinty ( later to become the Diceman ), hair cutting, street fashion design studio, audio art, street events, gigs and random acts of fun in public places.

Thom reportedly replied, " I can assure you that Spain pivoted precisely — not in the area of — but exactly there where the Railway Station in Perpignan stands today ".

In his Allmusic review, music critic Thom Owens wrote " the core of the album is Fleck & the Flecktones ' dynamite instrumental improvisations, where they can demonstrate the true range of their eclecticism and talent.

Old Mr. Thom himself had stopped at the service station for a grease job, Wally confessed, and couldn't get one because there were cars on the pits waiting to be repaired.

The lack of artifacts caused concern for some archaeologists and the petrofabric analysis was inconclusive, but further research at Maes Howe and on the Bush Barrow Lozenge led MacKie to conclude that while the term ' science ' may be anachronistic, Thom was broadly correct upon the subject of high-accuracy alignments.

Thom Yorke, who wrote all the lyrics, explained this by saying the words could not be considered separately from the music.

In 2010, it was reported that Yorke would be covering Peter Gabriel's song " Wallflower ", from Gabriel's fourth solo album Peter Gabriel 4 ( Security ), with Gabriel claiming, " Thom wanted to do a version of Wallflower, which I'm very curious to hear.

These conductions have received generally positive reviews, and are often considered quite unique, not quite fitting into any one musical genre: critic Thom Jurek has written, " There are no records like Butch Morris ' conduction sides, nor could there be, though he wishes there were.

" Wanniski suggested this position, as Thom Hartmann has clarified, so that the Democrats would " have to be anti-Santas by raising taxes, or anti-Santas by cutting spending.

It came to prominence when René Thom showed that cobordism groups could be computed by means of homotopy theory, via the Thom complex construction.

Angkor Thom seems not to be the first Khmer capital on the site, however.

In Patlabor the Movie 2, the opening scene appears to be based on the Angkor Thom, as said by Hayao Miyazaki in an interview with Animage magazine on October 1993.

" Thom Jurek of Allmusic later gave the album five of five stars and stated that: " A strong case could be made for Out of Hand as one of the Top 100 country records of all time.

( A madman, John Nichols Thom, claimed to be " Sir William Courtenay " in 1832, and stood for Parliament twice, proclaiming his right to the Earldom and the political platform of the extreme Philosophical Radicals.

3 is revealed to be a Thom Kallor who appears similar to his original pre-Crisis incarnation ( including the Starman history detailed above ), rather than the Star Boy that had most recently appeared in Legion of Super-Heroes vol.

The Thom ( p ) son's find the tablets and swallow them, thinking them to be aspirin, causing them to belch continuously, and grow long hair and beards that change colour.

Paul Augustine, revealing himself to be Pious in disguise, tries to kill Lindsey, but he escapes and makes his way through Angkor Thom.

Former head writer Thom Racina intended to hold off the couple's marriage and allow them to be separated by Scotty for six more months.

Del Vecchio announced that the first star guest designer for the new collection would be New York menswear designer Thom Browne.

This circle was one of the first to be analysed by Professor Alexander Thom to establish the likely use of standing stones as astronomical observatories.

" Reviewer, Thom Jurek praised the album highly, stating, " It's better than good, it's beyond expectation -- and it was high after Jasper County -- it's the best example of what a popular record -- not just a country one -- should aspire to be, period.

Thom Bell, and Kenneth Gamble & Leon Huff are considered the founders of Philadelphia soul.

Guests have included those who are generally considered left-of-center, including Noam Chomsky, Michael Moore, John Shelby Spong, Oliver Stone, Warren Beatty, Ralph Nader, Barbara Boxer, Al Gore, Madeleine Albright, Ben Cohen, George Galloway, Thom Hartmann, Naomi Wolf, Christopher Hitchens, and Al Franken.

Each entrance has a causeway over the moat with nāga-carrying devas and asuras similar to those at Angkor Thom ; Glaize considered this an indication that the city element of Preah Khan was more significant than those of Ta Prohm or Banteay Kdei.

Their eponymous first album sold very little by mainstream standards ( though 30, 000 records was a lot for an " underground " band ), yet is today considered a masterpiece by many, including influential artists such as David Bowie, Brian Eno, Iggy Pop and Thom Yorke of Radiohead.

" Writing for Allmusic, music critic Thom Jurek called the album " Evans, with Paul Motian and Scott LaFaro, was onto something as a trio, exploring the undersides of melodic and rhythmic constructions that had never been considered by most ... Explorations is an extraordinary example of the reach and breadth of this trio at its peak.

The building is considered one of the more important works of architect Thom Mayne, who won the Pritzker Prize in 2005.