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Description
Rational Homotopy Theory IIThis research monograph is a detailed account with complete proofs of rational homotopy theory for general non simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the
This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions.
This monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof.
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4.7 ★★★★★
Based on 24 reviews
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Product Reviews
★★★★★ 4
Interesting
Format: Kindle
This was a very captivating book once you got into it thoroughly. But the third person perspective was a bit hard to get used to. But as you got into it and followed the different characters, it was interesting and filled with intrigue, conflict and forbidden love.
I can’t wait to read the next one and to complete the series.
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Reviewed in the United States on November 12, 2022
★★★★★ 5
OUTSTANDING
Format: Kindle
This was very, very good. The world is vast and characters are complex. There is a good plot with a whole lot going on. This is well written. Good twists and turns and some heart breaking moments. You will love these characters, they have heart and loyalty. I am hoping that there will be several more books. We've yet to see anything from the Sea Court but only a mention of them here and there. The Wood Court was given a quick couple of scenes, and only as far as some warriors, we've yet to enter their court and the Shadow Court, I'm not sure if they will be a force for good or bad, but they definitely will play a much bigger role moving forward. This is primarily the Ice and Air Courts. Told in multiple views, which I loved, it gives you a chance to see things from different eyes. There's alot of political maneuvering and deception. I loved it and will pick up the next book as it becomes available. If you like The Fae and the courts, you should love this. I think the author has mucn in store for us.
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Reviewed in the United States on March 8, 2020
★★★★★ 4
Definitely worth the read!
Format: Kindle
After taking a deep breath and taking in that wicked twist of an ending, I have finally composed myself. My first thought when I started this book was that I love Reyna's character. I was intrigued by her connection with her familiar and the Ruin that is plaguing her land. It came as no surprise that she took her sister's place in an attempt to protect her. When they reach the Air Court everything slows down. This is where it was iffy for me. First of all, I like multiple POV's in books however 7 is a bit much. It starts to interrupt the story line. I felt like I was finally making progress connecting with one character, then it was switched to another person. I felt they all had necessary or pertinent information but not necessarily were they all POV worthy. The only other thing that annoyed me was that Reyna constantly was " trapped." She would rush off without thinking, only to need rescuing. She is brilliant in a fight, but she really doesn't think through anything. Lorcan is amazing. I know he might be on the "bad" list, but his background is so interesting. Eislyn(Reyna's sister) is really so sweet, but calculating. I enjoyed her and Thane's dialogue. The author did an amazing job with the imagery in this book. Everything was so detailed it was easy to fall into the scene. I love unexpected twists and while part of the ending I expected, I wasn't expecting how it took place. All in all, I found it very entertaining and I am very invested in continuing this series.
Favorite quotes:
"The truth may be twisted but never false."
"Who was she if she was not the enemy of the Air Court? What was her purpose of she no longer has that?"
"In a war-torn land, love was always a lie."
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Reviewed in the United States on March 4, 2020
★★★★★ 5
Great Read!!! Great story!!!
Format: Kindle
The series is long, but Ms. Wolfhart does a fantastic job of weaving this tale while bringing so much to the characters. Surprises and plot twists along the way to keep you intrigued. There is some graphic sex, but is no way the focal point. Grammar was excellent (a rare find with a lot of self publishers) with only a few noted errors. I rarely give 4 stars, let alone 5.
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Reviewed in the United States on April 30, 2021
★★★★★ 3
Sadly, DNF
Format: Kindle
I read this thru KU. I LOVED the synopsis. And then I began reading... and it was a DNF at 68% after picking it up and putting it down several times because I really loved the main female character.
*****SPOILERS*****
Pros:
The world is unique, intriguing and fun. The primary female character is bad-a** but not a b*tech or a mary sue. The primary female has depth. I really want to know what happens to her even tho it's been weeks and I don't remember her name. The villains to the point I read are pretty good -- an ever present threat of mysterious and possibly many culprits.
Cons:
Way, way too many points of view. I stopped counting at 7. It's the prime reason why I don't care about most of the characters or remember their names even when I like them. There's just too many points of view so almost none of the characters have enough book space for the author to properly develop them. This literally killed the book for me. Actually it killed my desire to read. For weeks.
The main male is more villain than hero. He agreed to marry the main female then locks her up & eschews her for her sister, all while bad mouthing her as unfit to rule when he never spent any time with her getting to know her. He is actually unfit to rule as he is blind to the woes of his own kingdom and starts off a peace mission to secure a ceasefire through marriage by murdering an inn full of people in her country for no real reason. Plus, he constantly makes promises he does not keep. And it's gross of him to pine for the sister behind the main female's back.
*****
As much as I really wanted to see what happened to the main female character, it wasn't enough for me to keep trying to slog thru this book. There was a lot of potential here that just fell short.
Hence, 3 stars.
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Reviewed in the United States on June 19, 2021