In the mathematical theory of knots, the unknot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied into it. To a knot theorist, an unknot is any embedded topological circle in the 3-sphere, ambient isotopic to a geometrically round circle, the standard unknot; the unknot is the only knot, the boundary of an embedded disk, which gives the characterization that only unknots have Seifert genus 0. The unknot is the identity element with respect to the knot sum operation. Deciding if a particular knot is the unknot was a major driving force behind knot invariants, since it was thought this approach would give an efficient algorithm to recognize the unknot from some presentation such as a knot diagram. Unknot recognition is known to be in both NP and co-NP, it is known that knot Floer homology and Khovanov homology detect the unknot, but these are not known to be efficiently computable for this purpose. It is not known whether finite type invariants can detect the unknot.
It can be difficult to find a way to untangle string though the fact it started out untangled proves the task is possible. Thistlethwaite and Ochiai provided many examples of diagrams of unknots that have no obvious way to simplify them, requiring one to temporarily increase the diagram's crossing number. While rope is not in the form of a closed loop, sometimes there is a canonical way to imagine the ends being joined together. From this point of view, many useful practical knots are the unknot, including those that can be tied in a bight; every knot can be represented as a linkage, a collection of rigid line segments connected by universal joints at their endpoints. The stick number is the minimal number of segments needed to represent a knot as a linkage, a stuck unknot is a particular unknotted linkage that cannot be reconfigured into a flat convex polygon. Like crossing number, a linkage might need to be made more complex by subdividing its segments before it can be simplified; the Alexander-Conway polynomial and Jones polynomial of the unknot are trivial: Δ = 1, ∇ = 1, V = 1.
No other knot with 10 or fewer crossings has trivial Alexander polynomial, but the Kinoshita-Terasaka knot and Conway knot have the same Alexander and Conway polynomials as the unknot. It is an open problem; the unknot is the only knot whose knot group is an infinite cyclic group, its knot complement is homeomorphic to a solid torus. Knot Unlink "Unknot", The Knot Atlas. Accessed: May 7, 2013. Weisstein, Eric W. "Unknot". MathWorld
For information on all College of Charleston sports, see College of Charleston CougarsThe Charleston Cougars baseball team is a varsity intercollegiate athletic team of the College of Charleston in Charleston, South Carolina, United States. The team is a member of the Colonial Athletic Association, part of the National Collegiate Athletic Association's Division I; the team plays its home games at CofC Baseball Stadium at Patriot's Point in Mount Pleasant, South Carolina. The Cougars are coached by Chad Holbrook, the head coach at the University of South Carolina; the College of Charleston baseball team has been a member of NCAA Division I since 1991. The Cougars have won five regular season conference titles and two conference tournament championships, one in the Southern Conference and one in the Colonial Athletic Association; the Cougars have appeared in the NCAA Division I Baseball Tournament seven times, most in 2015. They have advanced to the Super Regional round of the NCAA Tournament twice, accounting for their deepest postseason run.
The Cougars swept the 2006 Lexington Regional and the 2014 Gainesville Regional, before falling to Georgia Tech and Texas Tech, respectively. From 2009 until 2015, the Cougars were coached by a former player for Charleston. During Lee's tenure at CofC, the Cougars went 276–145, qualifying for the NCAA Tournament in four of Lee's six seasons. Lee coached three players that were drafted in the first five rounds in the MLB Draft: Taylor Clarke, Carl Wise and Heath Hembree, who reached the MLB in 2013. Lee left Charleston after the 2015 season to take the same position with the Clemson Tigers. Charleston has produced 27 college All-Americans and 62 professional players, including Brett Gardner of the New York Yankees. Since 2004, the College of Charleston has the 13th best winning percentage in all of Division I baseball. Charleston's history since joining Division I in 1991. Charleston has appeared in the NCAA Division I Baseball Championship seven times, most in 2015 when the Cougars lost in the Tallahassee Regional final to Florida State.
Charleston's overall record in the NCAA Tournament is 14–14. The College of Charleston has had 54 Major League Baseball Draft selections since the draft began in 1965. In 2015, pitcher Taylor Clarke eclipsed outfielder Brett Gardner as the highest Charleston player drafted, as Clarke was the first pick of the third round which bested Gardner's 109th overall selection in the third round of 2005. List of NCAA Division I baseball programs Official website
Thikse Gompa or Thikse Monastery is a gompa affiliated with the Gelug sect of Tibetan Buddhism. It is located on top of a hill in Thiksey 19 kilometres east of Leh in Ladakh, India, it is noted for its resemblance to the Potala Palace in Lhasa, Tibet and is the largest gompa in central Ladakh, notably containing a separate set of buildings for female renunciates, the source of significant recent building and reorganisation. The monastery is located at an altitude of 3,600 metres in the Indus Valley, it is a twelve-storey complex and houses many items of Buddhist art such as stupas, thangkas, wall paintings and swords. One of the main points of interest is the Maitreya Temple installed to commemorate the visit of the 14th Dalai Lama to this monastery in 1970. In the early 15th century, Je Tsongkhapa, the founder of the Gelug School - called "the Yellow Hats" - sent six of his disciples to remote regions of Tibet to spread the teachings of the new school. Tsongkhapa gave one of his disciples, Jangsem Sherab Zangpo, a small statue of Amitayus, containing bone powder and a drop of Tsongkhapa's own blood.
Tsongkhapa directed him to meet the King of Ladakh with a message seeking his help in the propagation of Buddhism. The King, staying in the Nubra Valley near Shey, loved the gift of the statue. After this meeting, the King directed his minister to help Sherab Zangpo to establish a monastery of the Gelug order in Ladakh; as a result, in 1433, Zangpo founded a small village monastery called Lhakhang Serpo "Yellow Temple" in Stagmo, north of the Indus. In spite of his efforts, the lamas who embraced the Gelug order were few, although some of his disciples became eminent figures over the years. In the mid 15th century, Palden Zangpo continued the monastic work started by his teacher, Sherab Zangpo, he decided to build a larger monastery here, dictated by an unusual event that occurred while choosing a site. Legends narrate that Tsongkhapa had predicted that his doctrine would prosper on the right bank of the Indus River; this prediction came true. This was followed by others such as Spituk Monastery and Likir Monastery, which are situated on the right bank of the Indus.
According to legend, Sherab Zangpo and Palden Zangpo were performing some sacred rituals near the Yellow Temple. The torma offerings were taken to a rock outcrop to be thrown down to the valley; as they were about to throw the torma into the valley, two crows appeared from somewhere and carried away the ceremonial plate with the offering of torma. They placed the torma at a location on the other side of the hill; when Palden Zangpo and his disciples began looking for the torma, they reached Thiksey, where they found that the crow had placed the torma on a stone in perfect order and in an undisturbed condition. Palden took this finding as a divine directive to build the monastery here; the new Thiksey monastery was located a few kilometres away from Stagmo, on a sacred hill above a village of the same name. The monastery is believed to have been built on the site of an earlier Kadam establishment or as a daughter house of the small chapel of Stakmo about 7 kilometres to the north. Rinchen Zangpo is known to have built a temple named Lakhang Nyerma at Thiksey dedicated to the protector Dorje Chenmo.
Today, all are some ruins. Thiksey grew in prominence in Ladakh, second only to Hemis Monastery, administering ten other monasteries in the region, such as Diskit, Spituk and Stok; the monastery came to own or control 1,327 acres of land and some 25 villages became attached to the monastery. In around 1770, the lama of Hanle Monastery dictated that his elder son should inherit the throne of Ladakh while other princes should be lamas at Thikse and Spituk; as a result, princes such as Jigsmet Namgyal served as lamas at Thikse. Restoration of the old monasteries in Ladakh, including the Thiksey Monastery, is being carried out by the Archaeological Survey of India, at the request of the concerned Monastery administration. This, has not been without its controversy, it is said that the traditional mud and stone courtyards have been changed to granite, which has marred the brightness of the place. The restored right wing of the monastery involving construction of new kitchen, the dining hall for the monks by replacing the old traditional central courtyard has caused dissonance to the entire old edifice of the monastery.
As a result, a balance to the restoration and renovation works has been sought to retain the old order in consonance with the new works. Thikse Monastery is the largest such structure in central Ladakh. Located on a hill slope, its building are arranged in an ascending order of importance and are well spaced, from the foot of the hill housing the dwelling units to the top of the hill enshrining the monasteries and potang of the chief lama; the architecture of the monastery resembles the Potala Palace in Lhasa, the former official seat of the Dalai Lamas. Thus, Thikse Monastery is known as'Mini Potala'; the motorable approach road from the valley passes through the east side of the Thikse Monastery's main building. There is statue of the Tibetan protective deity on this path at the entrance at the lower level; the highest level of the complex has a stupa. The monastery precinct at the foot of the hill has a courtyard from where a flight of steps leads to the main monastery (one